Private shuttle or train trip in Genrva

The train is scenic, but comparatively slow, since you are climbing into the Alps
and there are 1 or 2 connections. A direct shuttle will take maybe 1.5-2 hours at
the most.

A private shuttle will probably run about 250-300 EUR one way, but this does
not include a guide.

The question is what do you think you need the guide for, and what time of the
year are you thinking of going? Taking the Aiguille du Midi up, looking around,
maybe the Panoramique to Italy, getting back to Chamonix, maybe the Montevers
train to the glacier, and just wandering around the town, seems like a pretty full
day to me, and probably doesn't need a guide. But some of these things may
not be running in off season.

So I think your budget is probably reasonable in any case, but may be excessive
depending on what you want to do in Chamonix.

While your most likely return route is back to Geneva and then a train to Lausanne,
there are ferry boats that go across the lake from Thonon or Evian as well.

You might look into a shuttle from GVA to Chamonix. We used AlpyBus some years ago in the opposite direction and it was far more efficient than the trains would have been.

Chamonix is the kind of place you want a clear day for, IMO, but deciding last minute may make it challenging to schedule a shuttle. There are some nice mountain trips you can take from Vevey and Montreux, just east of Lausanne. Rochers des Naye https://www.myswitzerland.com/en-us/experiences/rochers-de-naye/ and Les Pléiades https://www.myswitzerland.com/en-us/destinations/les-pleiades-daffodils-and-stars/. If the weather is great, you can easily take the train to either and if the weather is poor, you can enjoy city activities in Geneva, Montreux, and Lausanne.

Thanks for the input. They are very helpful.