The C-clamp method works with an older quality C-clamp. I wouldn't try it with some of the newer cheapo chinese cast C-clamps. Those will snap if you just drop one unloaded onto a wood workbench from more than 12" inches. Drop one on a concrete floor and they shatter into multiple pieces.

the other problem with a C-clamp is the thread pitch. A C-clamp has a very coarse thread pitch of like 6-8 threads per inch where a good press like the wheelsmith or even this Harbor Freight conversion will have something on the order of 25-30 tpi or more. That is just leverage. With more TPI you have a ton more leverage for each thousandth of an inch you need to move the cotter until it gives way.