Braze welding uses a bronze or brass rod and has either flux added to the rod commercially on the outside or you dip the heated end of the bare rod into flux. Dip the heated rod into the powder and it sticks. This means that the joint between the two parts to be welded need a bit of a bevel on the surfaces and also need a little gap between them. Then you set your round rods in here and it always holds them in line. Silver brazing is what would be best here.
Silver is very low viscosity and so flows easily into tight joints.
For this it is best to buy some commercially. The parts are then placed in contact with each other in a way that they will not be bumped or moved. Then heat them up to an almost dull red but mainly watch the flux. When the flux gets watery looking, touch a thin rod of the silver braze alloy to the side of the joint. Capillary action pulls the molten filler material into the joint, just like water is pulled into a paper towel.