I've been loading 45 Colt for years. I just checked the SAAMI drawing and it isn't a tapered case. As straight as it can be.
There is no difference between regular dies and Cowboy dies. Cowboy usually refers to loading light, in my experience. No point in beating yourself or the gun up. And Cowboy targets are generally steel.
I use the RCBS 3-die set and load on an RCBS Pro2000. I load SNS Casting 250 gr LRNFP. I shoot them out of a Henry Big Boy and a pair of Vaqueros. I recommend checking a load manual or two for load data. For years I loaded Unique. I am about out, and have a lot of TiteGroup so am starting to load that under my 250 gr. Depending upon velocity hardness matters, to reduce leading in the barrel. I find SNS does a good job with their hardness and I have little leading problems with their bullets. If they do lead up I use my DIY lead remover to scrub it out. On the other hand there are plenty of options for coated bullets, if you prefer that. I also recommend case lube, as the cases are really long.
I recently took up Cowboy and definitely load light. You'll find plenty of opinions as to the best powder and so on, for Cowboy. I am in no position to recommend one Cowboy powder over another, if that is what you're looking for. When I started loading light for Cowboy I found I had a lot of unburned Unique. Lighter loads means lower pressure and Unique does better at higher pressure. TG does better IMHO.
As with all revolvers, the round uses a roll crimp. I just followed the RCBS instructions long ago and never changed. My standard OAL is about 1.600, which you'll see commonly in the load manuals.
Again, read the directions that come with the dies and have fun. BTW, I chronograph pretty much all my loads, pistol or revolver.
