Giving a safety/double-edge razor a try...

[LazyPrizm]

I wound up liking and using DE Bic blades, which are pretty cheap on Amazon in a 30-pack. Had decent luck with some random USA-made (!) Gillettes I found once in a drug store as well. Never found a blade that lasted more than 3-4 shaves TBH.

I used to joke about them being "grandpa razors", but a few months ago my dad actually gave me my grandpa's razor! Haven't tried it yet, it needs some TLC first due to rust & neglect.

 

[sciphi]

Update:

I'm still liking the DE razor experience. I recently purchased a 100-pack of Feather blades, as they seemed to work the best on my face. I'll probably change them after every 2nd shave, as I get nicked less with a sharp blade that slices the hair compared with a duller blade that tears the hair. They also got wife approval.

Other blades I liked were Gillette Goals, Derby Extras, and surprisingly, Trig blades. Those blades gave good shaves. The wife ixnayed those because of my face feeling like coarse sandpaper. The Feathers minimized that, so they were okay.