The existing star codes -- the ones that are configured by default-- do not have anything like this, so there's nothing you can do there. The closest might be *72 for Call Forward All but you have to enter the forward to number in addition to the star code, and it sounds like your GV is already setup to forward to your cell phone.
If you were up for some tweaking and experimentation, you might get it working with a star coder you create. Star codes are really implementations of macros in the obi's logic, for example this is what *72 really implements: "*72, Cfwd All, coll($Cfan), set($Cfa,1)". The third item in the comma delimited list is what does the call forwarding work. Look for "Star Code Script Variables (VAR)" in the device admin guide. What I'm suggesting is you might setup some forwarding to a line that never answers (the telco port on your Obi110?), you are going to have to figure this out on your own. One tip is one star code can call another star code, that might help.
P.S: You could also take an out of the box approach and use Dog Whisperer principles to train your dogs to not get excited at the sound of a phone ringer.