Sorry ignore my answer above, I can't edit it and it isn't completely correct. Here's my updated answer:
Just to make sure I understand you correctly if you mean only the controller itself, yes it will fit either one. Foot controllers are pretty much generic and can be used on many machines. I have wired one from my 1948 Singer 15-91 onto a 1960's Japanese made White.
Only problem I can see is if your 301's foot controller plugs into a 2 or 3 pin terminal. This is a 2 prong wire
http://shop.sew-classic.com/Cord-Sin...rol-197628.htm. If both the Featherweight and 301 have a 3 pin terminal like this
http://shop.sew-classic.com/Cord-Set...ers-SCE123.htm than don't need to do any rewiring. You can plug it directly into the Featherweight.
Edited to add
Cari answered while I was typing my update.