I scored this Cobra aero bottle of E-Bay but when it arrived , it turns out the cap is broken off at plastic tether and gone missing:

I’m only out $8 bucks but it really chaps my hide. Is there anything that can be done to salvage this bottle?
A separate question is that the bottle seems to be a bit short for the cage. Were there different models of these Profil bottles or did they all fit like this?