Couple of idle thoughts...
1) Baboo ran a service from Oxford to Geneva last winter using a Dash-8. Apparently loads were very good with a service running each Saturday. They didn't repeat it as I believe they thinned down their fleet.
2) Eastern tout for this kind of work over their website - they have low utilisation over the weekend but Friday night is still going to be peak for them.
3) I think - in all honesty - if you look where the line lies for the cash rich/time poor, they'll either make do with what they have (like train via Geneva), go to a different resort with shorter transfer from GVA, go for longer, or just get on the phone to Blink/NetJets.