“As far as everyone is concerned, the US (your people, collectively) gave its word. No matter how you kick back at that, it is what it is.”
We have a saying in the US: “Not worth a bucket of warm piss.” Which is what a Bill Clinton promise and an agreement not ratified by the US Senate are worth.
You are bound, regardless. You cannot, individually, reject such a commitment and retain your credibility in the wider world. No amount of private rage will shift that, among peoples who are not you.
As for Clinton or not-Clinton - Ronald Reagan, or any US President, would have signed that, word for word. It meant a major reduction in nuclear risk, which was what he was after. It was a no-brainer at the time, a gimme.