Q:

Why didn't Ozymandias kill the Comedian with a gun, or a knife? 

It just seems to me he could have gotten over the fight much faster with either of it, and made much less of a mess doing so. 

A:

Firstly, Veidt did not want this to look like an assassination.  In fact, he tried to make it like a burglary gone wrong - and what kind of burglar carries a knife or a firearm around?  
Granted, the "burglary" version isn't too believable - even the police doesn't find it convincing, but they still decide not to dig too deep because they discover Blake had some ties to some secret agencies, and the whole affair might be above their level of competence. 
The burglary story is just good enough for the press and for their superiors, so the police decides to let it slide.  
Rorschach goes one level past the burglary version and decides it's some sort of killer who is hunting former masked adventurers.  For Rorschach, Veidt does indeed have a "mask hunter"  ready, one he hires to assassinate himself.  By then Rorschach is also satisfied and occupied elsewhere, so Veidt is completely off the hook. 
Lastly, Ozymandias had a grudge against the Comedian - the two had an encounter before which resulted in a fight (which is shown in Before Watchmen - Ozymandias), one the Comedian won "in the short term" (Veidt's words).  Veidt appears to have analysed Comedian's fighting style, and let him win that time.  It appears he wanted to test his analysis, and to settle the grudge.  He was sure he'd be able to do it with his bare hands, as he was sure of many other things.