In the config:

DNS = <public-resolver>,<private-reslover>

...wouldn't work?

Edit: per discussion on r/Wireguard, looks like one soln is to run dnsmasq locally on ::53 and forward public queries to the VPN/DNS provider of your choosing and resolve private queries locally.

https://www.reddit.com/r/WireGuard/comments/cmhap6/use_both_...