My suggestion if you want 20 Hndy LR, is to get 20 Hndy LR. Lots of online retailers have them, or can get them. For example, Cabelas has them on backorder (usually that mean 1-2 weeks delay) for 35$/box of 20. Oher retailers can usually get them on request.
Even with a Lee Loader, you're looking at 50$ for the loader, 40$ for a pound of powder, and 25$ for the bullet puller (a cheapo kinetic). That's 3-4 years of LR ammos right there.
I think your way would work though. If you pull the bullets from your ammos, the brass won't expand like when it's shot, so it'll feed and chamber correctly. The fact that it neck sizes only will be irrelevant. And I would also re-use the pulled bullets, it's not like they're match-grade ammos to begin with, and a kinetic puller doesn't really harm bullets anyway.
Ganderite's way of buying a cheap used press and a set of Lee dies (also used if possible) is the best way to go imho. It'll cost you 100-120$ instead of 55$ for the loader, but it'll 100% work for you, and if you buy used you can make a few hundred rounds, then sell the whole stuff for about as much you paid for it.