You can.
You have to enable Bluetooth in the SteamVR Settings, and they'll automatically turn off when you quit VR, and back in when you start it up again. Only downside is (at least for me) when you don't use it for a longer time the connection seems to drop, and they won't turn on automatically anymore. But nothing that can't be fixed with a quick un- and replug
I've set up several instances in circumstances like yours. The easiest way is to create a duckdns domain for yourself, and install their updater on one of your systems, to keep your external IP up to date with their DNS-Servers. Then you can use a DNS-Provider of your choice (I use Cloudflare) to create a "CNAME" DNS Record, that basically just tells a browser to redirect from your domain to the IP Address of the duckdns domain. That way you can have an automatically updating public IP behind your domain name. Then you "just" have to set up a reverse proxy (I use Nginx Proxy Manager, but there are newer and easier alternatives), and create the correct port forwarding rules in your router/firewall, and you should be good to go