Q:

Suppressing node styles for certain nodes

Using the following code
\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{verbatim}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{arrows, arrows.meta, positioning, calc, intersections, decorations.pathreplacing, decorations.pathmorphing, decorations.markings, shapes, shapes.misc, shapes.symbols, shapes.geometric, patterns, backgrounds, trees, shadows}
\begin{document}
\begin{frame}[t]
\frametitle{}
\small
\begin{tikzpicture}[scale=.9, transform shape, every node/.style={draw, very thick, black, rounded corners=5pt, inner sep=5pt, align=center, drop shadow}]
\node at (0,0) (invp){}
([shift={(0:3.5cm)}]invp.center) node (fin){}
([shift={(0:3.5*.5cm)}]invp.center) node (inu){}
([shift={(-90:1.8cm)}]inu.center) node (ind){}
([shift={(0:3.5cm)}]fin.center) node (shar){}
([shift={(0.:3.5cm)}]shar.center) node (invo){}
;
\node[rectangle, blue, outer color=blue!40, inner color=white, text width=1.68cm, minimum height=2cm] at (invp.center) {xxxxxx};
\node[rectangle, purple, outer color=purple!40, inner color=white, text width=1.4cm, minimum height=2cm] at (fin.center) {xxxxxx};
\node[rectangle,  green!40!black, outer color=green!70!black, inner color=white, text width=1.88cm, minimum height=2cm] at (shar.center) {xxxxxx};
\node[rectangle, brown!80!black, outer color=brown!60, inner color=white, text width=2.4cm, minimum height=2cm] at (invo.center) {xxxxxx};
\node[black, draw=none] at (ind.center) {Invest};
\draw[line width=1.4mm, black!60!white, latex'-, shorten >=26pt, shorten <=30pt] (invp.center) -- (fin.center);
\draw[line width=1.4mm, black!60!white, -latex', shorten >=30pt, shorten <=26pt] (fin.center) -- (shar.center);
\draw[line width=1.4mm, black!60!white, -latex', shorten >=38pt, shorten <=32pt] (shar.center) -- (invo.center);
\end{tikzpicture}
\end{frame}
\end{document}

How can I make certain nodes not use the node style definition? 
For example defining the nodes inu and ind without drawing the border and drop shadow, and displaying the text "invest" without the drop shadow

A:

Here I put the \node commands of these two node to a scope and redefine every node inside that scope. 
\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{verbatim}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{arrows, arrows.meta, positioning, calc, intersections, decorations.pathreplacing, decorations.pathmorphing, decorations.markings, shapes, shapes.misc, shapes.symbols, shapes.geometric, patterns, backgrounds, trees, shadows}
\begin{document}
\begin{frame}[t]
\frametitle{}
\small
\begin{tikzpicture}[scale=.9, transform shape, every node/.style={draw, very thick, black, rounded corners=5pt, inner sep=5pt, align=center, drop shadow}]
\node at (0,0) (invp){};
\node at ([shift={(0:3.5cm)}]invp.center) (fin){};
\begin{scope}[every node/.style={very thick, black, rounded corners=5pt, inner sep=5pt, align=center}]
\node at ([shift={(0:3.5*.5cm)}]invp.center)  (inu){};
\node at ([shift={(-90:1.8cm)}]inu.center)  (ind){};
\node[black, draw=none] at (ind.center) {Invest};
\end{scope}
\node at ([shift={(0:3.5cm)}]fin.center)  (shar){};
\node at ([shift={(0.:3.5cm)}]shar.center)  (invo){};
\node[rectangle, blue, outer color=blue!40, inner color=white, text width=1.68cm, minimum height=2cm] at (invp.center) {xxxxxx};
\node[rectangle, purple, outer color=purple!40, inner color=white, text width=1.4cm, minimum height=2cm] at (fin.center) {xxxxxx};
\node[rectangle,  green!40!black, outer color=green!70!black, inner color=white, text width=1.88cm, minimum height=2cm] at (shar.center) {xxxxxx};
\node[rectangle, brown!80!black, outer color=brown!60, inner color=white, text width=2.4cm, minimum height=2cm] at (invo.center) {xxxxxx};
\draw[line width=1.4mm, black!60!white, latex'-, shorten >=26pt, shorten <=30pt] (invp.center) -- (fin.center);
\draw[line width=1.4mm, black!60!white, -latex', shorten >=30pt, shorten <=26pt] (fin.center) -- (shar.center);
\draw[line width=1.4mm, black!60!white, -latex', shorten >=38pt, shorten <=32pt] (shar.center) -- (invo.center);
\end{tikzpicture}
\end{frame}
\end{document}

I don't know if this is what you are looking for. 

Edit: This is the \tikzset solution:
\documentclass{beamer}
\beamertemplatenavigationsymbolsempty
\usepackage{verbatim}
\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{arrows, arrows.meta, positioning, calc, intersections, decorations.pathreplacing, decorations.pathmorphing, decorations.markings, shapes, shapes.misc, shapes.symbols, shapes.geometric, patterns, backgrounds, trees, shadows}
\tikzset{
    escape/.style={very thick, black, rounded corners=5pt, inner sep=5pt, align=center},
    notescape/.style={draw, very thick, black, rounded corners=5pt, inner sep=5pt, align=center, drop shadow}
}
\begin{document}
\begin{frame}[t]
\frametitle{}
\small
\begin{tikzpicture}[scale=.9, transform shape]
\node[notescape] at (0,0) (invp){};
\node[notescape] at ([shift={(0:3.5cm)}]invp.center) (fin){};
\node[escape] at ([shift={(0:3.5*.5cm)}]invp.center)  (inu){};
\node[escape] at ([shift={(-90:1.8cm)}]inu.center)  (ind){};
\node[notescape] at ([shift={(0:3.5cm)}]fin.center)  (shar){};
\node[notescape] at ([shift={(0.:3.5cm)}]shar.center)  (invo){};
\node[notescape,rectangle, blue, outer color=blue!40, inner color=white, text width=1.68cm, minimum height=2cm] at (invp.center) {xxxxxx};
\node[notescape,rectangle, purple, outer color=purple!40, inner color=white, text width=1.4cm, minimum height=2cm] at (fin.center) {xxxxxx};
\node[notescape,rectangle,  green!40!black, outer color=green!70!black, inner color=white, text width=1.88cm, minimum height=2cm] at (shar.center) {xxxxxx};
\node[notescape,rectangle, brown!80!black, outer color=brown!60, inner color=white, text width=2.4cm, minimum height=2cm] at (invo.center) {xxxxxx};
\node[black, draw=none] at (ind.center) {Invest};
\draw[notescape,line width=1.4mm, black!60!white, latex'-, shorten >=26pt, shorten <=30pt] (invp.center) -- (fin.center);
\draw[notescape,line width=1.4mm, black!60!white, -latex', shorten >=30pt, shorten <=26pt] (fin.center) -- (shar.center);
\draw[notescape,line width=1.4mm, black!60!white, -latex', shorten >=38pt, shorten <=32pt] (shar.center) -- (invo.center);
\end{tikzpicture}
\end{frame}
\end{document}

