The magnet is not a great idea, they tend to be quite brittle, especially the rare earth type commonly available now. That being said, you're pressing shafts out of fishing reels -- how much force are we really talking about here anyway? Probably not a lot, and in that case the magnet may not be at great risk. It would require a very flat interface though, and the potential for getting off-center and popping out of the assembly at the least opportune moment would be a bit scary.
Thinking about my hydraulic press at home, I think the end is hardened somewhat. If I were to contemplate a similar thing for my own use I suspect I would make an adapter (an suitably sized iron pipe cap, maybe) that I could marry with the chuck (drill through for a bolt or thread depending on the chuck) and that would slid over the outside of the ram a short distance. I could use a set screw or two in from the side to hold it from falling off.
-frank