That’s crazy dude. I think it’s pretty silly for you to refuse a vasectomy in that situation but if you are going to stand fast then check out an IUD for your wife.
If the choice was vasectomy, condoms, or no sex, I’d probably go condoms, vasectomy, no sex in that order.
As in, “condoms beating vasectomy by half a length with no sex recording a DNF (maybe even a DNS).”