He needs to get one now. If he doesn’t want kids, it’s his turn to pick up the burden. Now. Right fucking now. Also, he needs to wear a condom every time until the vasectomy is complete.
He’s not meeting you halfway! And he should have been proactive! Why are you trying to talk reason to him? Why didn’t he get one himself as soon as he was certain he didn’t want kids?
Women should not be the only ones bearing the burden. It’s way simpler for men.