Thanks to Jonas's answer I discovered the Bergfex Swiss ski resorts list. With a bit of fiddling, I was able to get up a map showing all the resorts that still had lifts running this weekend.
Based on that, the only sensible looking one was Engelberg/Titlis, which still had its high red and black runs open. It's fairly easy to get to, and by train from Zurich it was 2 hours from Zurich HBf to the resort. The train ride from Luzern to Engelberg was very picturesque, and there were a lot of tourists on the train. There's a free shuttle bus from Engelberg station to the bottom of the ski lifts, or it's a 10 minute walk.
There are a few ski hire places in Engelberg, the one I went to was just before the ski resort, and they were very friendly and helpful. It was CHF 49 for a day's hire of decent skis with poles. It was two gondola stations up to the start of the snow, then two more up to the top (10,000 feet). Most of the people there weren't skiers, but instead tourists coming for the views and the snow tubing. (Huge numbers of Indians - I'm told it's something to do with Bollywood?). The only downside of this is that they were going to a ski resort for the first time, and didn't really know how to behave or what to expect, which slowed things down...
As might be expected, the lower runs were pretty sludgy by the end of the day, but the highest ones stayed pretty good. Not a huge amount of variety with just a few runs and lifts open, but the weather was stunning, and I got one last day's skiing in this year! The slopes were fairly quiet but not deserted, and the chair lifts pleasantly quiet (just a shame about the gondolas shared with the sightseers)
For someone elsewhere in Switzerland, it should be easy enough to use the Bergfex list to find a resort near you that has runs+lifts open, and get that last bit of snow in before the summer hits!