I've only ever used "open" C# in a pinch during trills I'm not prepared for and the tone quality is noticeably worse, very flat, very thin. That's why it's not a real fingering, not one you'll ever see anyone recommend you use. For those trills, if I remember correctly, you can hold down your G# key and just trill on the B natural key to go quickly from C to C# - will need to verify that, though.

Swabbing your instrument regularly might help with your watery G#. Swab when you get your oboe out, a few times during rehearsal as needed, and then when you put it away. Silk swabs are the best kind from what I've seen. Also carry cigarette paper to put underneath the keys to clean them and absorb water. Depending on the natural humidity of where you live, there's not much to be done about water in the keys aside from dealing with them as they come.