Please, please make that call.
After being in an abusive relationship, I vowed I would never let that happen to me ever again.
I did a Clare's law request around 4 months into dating a subsequent partner. We'd had an argument and something about the way he behaved just didn't sit right with me, so I put the request in.
Around a week later, a lovely female officer called me and yes, there were several violent incidents she needed to tell me about. So that was that relationship ended instantly.
I know you said OP that you have no concerns about your partner, but this is really, really not a reason to not do it.
The phone call is discreet, he will never found out.
You said you are worried he would be hurt if he found out you'd put a request in. Why? That in itself is worrying. If he's a decent man he would understand your motivations. Please don't put upsetting a man above your children's safety.
If I found out (through a partner telling me) a request has been put in about me, I'd be confused yes, but ultimately I'd end up respecting my partner more for being a responsible person/parent and putting theirs and their children's safety first.
In addition, if anything is disclosed to you and you continue to have contact with your partner and allow him to have contact with your children, social services will look very unfavourably upon this and you will be considered to be failing to safeguard your children.
Please, please do it.