It wouldn't be him renewing Trident, though. The will of Parliament is clearly that it be renewed as a deterrent system, which - up to this point - it has done.
What he should be making clear to people is that is all it does - and if we ever launched it it wouldn't be because of a terrorist detonated nuke in London, or in order to "defend" us, it would be because the world was about to end.
If he wouldn't push the button under even the most unimaginably bad situation then it's no longer a deterrent and he should spend the cash elsewhere. And he should be open with parliament on that (if elevted) so they knew the score.