You‘d have to redirect all network usage (i.e. the sockets API or your platform‘s equivalent) through the custom stack, which is possible if you can rebuild the source or by using something like LD_PRELOAD for binaries, but can get very tricky in the general case.

There‘s an utility called SSHuttle that does something similar for SSH instead of Tailscale/Wireguard: It redirects all sockets usage to go through an SSH connection, to allow usage of SSH port forwarding without explicit SOCKS support on the app‘s side.