Swiss vacation in late May

"late May" and "luge run" might be a tricky combo, it is a bit early for the summer season.
But there is one in Kandersteg, so that would be a good reason to stop there, besides the Oeschinesee hike.
Your mention of that hike near Schwyz puzzles me, as the only mountain of that name I can find is near Interlaken.
Speaking of which, you should definitely plan some time in the Berner Oberland region south of Interlaken.
Possible route could be 3-4 nights in Wengen, 1 in Kandersteg if you like, then Glacier Express to Chur (1 night), Albula and Bernina railways to Varenna for lake Como (3 nights), final night in Milan.

I was afraid that late May would be pushing too early. The hike I was referring to is actually in Stoos, but its my understanding you can take the funicular from Schwyz to Stoos. It's called the Stoos Ridge Hike (think I had the wrong name above) from Klingenstock to Fronalpstock. Do you think hikes will be a problem at that time of year? The Kandersteg one looks great also. I guess I was thinking it might be more direct to Chur from Schwyz than from Kandersteg for the next leg of our trip. Please correct me if I'm wrong! Thanks in advance!

No, you are right, lake Luzern will be closer to the Bernina railway.
As for that hike in Stoos: I would like to go to Stoos someday, probably in winter, but I haven't been! There are plenty of hikes and excursions around Lake Luzern anyway, so that region would be a good base for a few days.
Late May isn't ideal for hiking higher elevations, but anywhere under 2,000 metres should be totally snow-free (and the mountains around Lake Luzern aren't that high).
If you have the time, rather than Chur, spend some time in/around Pontresina. Or if it's just for one night, Bergün is a lovely village right off the Albula Railway.

Thank You! Every little town I've seen online looks so charming!. I'm afraid of missing a hidden gem. We prefer the more relaxed, less crowded areas, rather than the big tourist hotspots, but still want the historic charm and beauty. With our timeframe, we realize we are going to need to be super selective and will still miss a ton of beautiful sites.
You mentioned Wengen in a earlier message. I had looked at that and thought it looked like a good base for a few days. Is it close enough to many other locations to travel from there daily as our base? Looks beautiful!

I mentioned Wengen, because most people consider the Berner Oberland region (where this village is located) to be the top #1 attraction in Switzerland thanks to the unique mountain scenery. It is one of a handful of car-free villages in the area, high above a deep valley and facing the impressive Jungfrau range.
If this is your first trip to Switzerland, that region comes highly recommended. Schwyz / Lake Luzern can wait for a future trip.

The Rodelbahn at Oeschinensee opened on May 8 last year:

https://www.oeschinensee.ch/rodeln/

That may or may not give an indication of what one can expect in 2022. It depends upon the opening of the gondola that takes people up to the lake, and that has not been set yet. They are still showing the 2021 summer schedule.

https://www.oeschinensee.ch/gondelbahn-sommer/

We like to stay at the Berghotel right at the lake, owned by the Wandfluh family for some 500 years. They are accepting reservations starting 26 May. We like the double room with lake view—-the view from the window is shown in the photo near the bottom of that page, immediately above the plate of food.

https://www.berghotel-oeschinensee.ch/berghotel-oeschinensee/

There is also a Rodelbahn at Grindelwald, at the top of the Pfingstegg lift.

https://www.pfingstegg.ch/index.php/en/activities/toboggan

Grindelwald may be a larger town that you want, and it is not car-free. But there are some adventure activities on offer at the First gondola. The First Flieger zip line and the glider ride are open all year; the Trottibike ride opens May 7 and the mountain carts a week later.

https://www.jungfrau.ch/en-gb/grindelwaldfirst/

The hike to Bachalpsee is easy but stunning, and it’s usually open by late May.

https://www.jungfrau.ch/en-gb/summer-sport/hiking/hiking-trail/first-bachalpsee-first/

And if that is open, other hikes in the area may be as well.

We have not been to Stoos, but it looks like the elevation is low enough (1330 meters) that you probably have a better chance of snow-free hiking there.

Thank you all so much for the insight! I think it's easy to go down a rabbit hole and get confused, but you have helped me focus. This is our first trip and I'm thinking you are right about Wengen and Lauterbrunnen. There are probably endless hiking opportunities around any one of them.