I’d go one better.
Decline to disclose if any questions come your way, written or verbal.
“Neither confirm nor deny” cuts both ways.
I’ve kinda been doing that with my employer. We have a daily form we have to fill out where they ask your vaccine status. I’ve never answered that question. So far I’m still working.
The day they insist I answer that question is the last day I’ll work for them. I’m pretty sure they know that.