This thread has covered pretty much of of my thoughts, but to summarize;
1) you
could use a bench top drill press as an arbor press and it would probably work OK for a while, but…
2) depending on how you set it up, how well built the press is, and how much pressure your die will require to perform its duty, you will…
3) get less than optimal results and probably…
4) introduce unwanted wear to your drill press, especially the bearings that are designed for rotation rather than compression.
As 1Hawkeye said, a quick trip to Harbor Freight (or someplace similar) will net you a cheap, probably $25 or less, arbor press that is made to do the job. Their smallest press is rated at 1/4 ton, IIRC, and will be more than you need. A more elegant (but expensive) solution would be one of the little purpose built presses from Sinclair or Harrell. Even thee smallest of the ones from HF is overkill, but will certainly do the job perfectly and cheaply. Why try to use your drill press in a way it wasn’t intended?
Froggie
PS While taking a course in machine shop, I built my own arbor press, making everything but 4 little machine screws from raw stock. I’m the coolest kid on the block when I use that!