I think you should think carefully and make the decision based on what you want, especially as you sound slightly distrustful of your partner and the longterm viability/longevity of the relationship.
I fully respect the decision to be childfree as a completely valid life choice which should stop being stigmatised and viewed as odd - and I have never myself believed in our experienced the much-famed 'biological clock' - but there are a few things in your OP that do strike me. Mainly that you sound anxious to get the decision over and done with, maybe because if you don't close off the option of having children, you may need to end your relationship with a man who doesn't want any, and begin to look for someone who does,mor go it alone? Ie, deciding you might want a child in future may bring the end of your current relationship, and this is unsettling you?
I'm struck also by you thinking your partner might end things and have children with someone else, and that your desire to get him to have a vasectomy is partly about closing that option off for him - as well, obviously, as removing the need for you to consider contraception. And leaving you technically capable of conceiving in a subsequent relationship...?
My own experience was of a happy longterm relationship with a man who shared my lack of interest in ever having children. I never felt broody, have suffered badly from depression, all family in a different country, and we were both very work and travel-focused, but we did ultimately decide to ttc when I was 40, because we thought it might be a nice thing to do. Honestly, we weren't that bothered, and were a bit taken aback when I conceived immediately. We now have a gorgeous, stroppy toddler, and life is differently rich.
I suppose all I'm saying is that while all those 'OOH, you'll change your mind!' comments (which I got for almost 20 years) are insulting and tiresome, and plain wrong for many people - there are things about your OP that suggest you're rushing yourself into a decision out of anxiety, rather than out of complete conviction that a child isn't for you...