weather and hotel bookings

I think you will find there is availability even last minute in October. You might not have the choicest rates nor rooms, but there should be something. We made a fairly last minute decision a couple of years ago to go to Lauterbrunnen for a few days at New Years, checking in on the 1st. Rates were high and choices were slim, but even last-minute we got a comfortable if not elegant room.

Staying 3 nights (or more) is often a good strategy in this area because if you have a better chance of hitting some good weather.

The area is subject to ever and quickly changing weather even in summer. I would keep your reserv and decide on monday based on weather forecast. If it is bad weather then cancel and stay somewhere nrby as lake brienz and if weather clears go for the day. The area is gorgeous but in a white out , not so.
U are wise to plan ahead.

As to your actual question - unless that mega hurricane over Cuba decides to send all its nastiness to Switzerland (that should be past in 9 days, and the UK tends to get the brunt, not central Europe), the middle of October in the Alps can be quite beautiful. A couple of weeks later or a month later will be shoulder season and could be less than pleasant but you should luck out during a part of your extremely short stay in the mountains. 2 nights only gives you one day if the weather picks that day to be uncooperative. Whenever we go to the Berner Oberland we stay for a minimum of 3 to 5 nights.

Any chance you can add a night?

Thanks for all the insight! If the weather is rainy/cloudy, I heard that it is not worth it to take some of the expensive high mountain trips. Any suggestions of other things to do in this area if the weather is rainy and cloudy?

The rain tends not to be constant. Best skies often in the morning, clouds bubble up after midday. If there is poor weather at the summit it may not be that way in a couple of hours. You may find that if the weather is poor at the Jungfraujoch the summit of Schilthorn may be different. If there is fog in the valley the middle and higher trails may be better.

Even if it is raining, light rain and fog, the walk between Mürren and Gimmelwald and the walk between Mürren and Grütschalp are both fine and scenic. Staying on that side, using the funicular up to Allmendhubel and looking around can be fabulous as long the rain is light. And perhaps the flower walk back down to Mürren (not many flowers at this time of year, but if there are any they are alpines).

Or if it is worse, a valley walk can be nice if you have the right clothes on or Trummelbach Falls or a ride on the lake.

Whatever the weather, unless you can't see them at all, the mountains are spectacular, especially from (IMHO) the Mürren side.