DH took himself off to get a vasectomy about 5 years ago, of his volition, when we knew our family was complete.
I didn't need to ask him. He offered, and was perfectly willing to take the 'risk' (minuscule, compared to anything I'd faced), because he is a decent, caring, loving husband, who was more than happy to step up to the plate in the contraception department.
He had seen me go through two pregnancies and childbirths, and figured it was his turn.
He was in and out, and now we have easy, uncomplicated sex, with no worry or risk of pregnancy.
I think any man who does any less is beyond pathetic - and make no apology whatsoever for my stance.
It's my absolute unapologetic position to think that any man who procrastinates, whines about the (relative to women's) low risks, and whinges and reneges is a sub-standard man, and I judge them whole-heartedly.
If your man falls into this latter category and you want to come on here and whine at how nasty I'm being, then bring it.
And to any man opting out on the 'my body, my choice' card - you're the weaseliest, lowest of the low. By opting out of any risk whatsoever, you force your partner to take the full risk load, and for that you should expect to be judged and found completely wanting.
Good luck OP - I hope your DP proves himself to be the decent type, willing to just get on and do it. 