Hi Julia -
<<"Is there an alternative way to visit Schilthorn or a recommendation for
another mountain trip in the Wengen area would be appreciated.">>
In order to best answer your question, we need to know your travel dates. There is only one way up to the Schilthorn from Mürren, the cableway, unless you climb on foot. It is an ascent of roughly 1340 meters. If you were able to hike it through the snow and ice ( not likely) during the time that the cableway is closed, you would find the the tourist services up there are closed.
The Jungfraujoch is an obvious answer. It is available e very day of the year. It is also very expensive. Theere a varying opinions on whetehr itis, as they say "worth it".
This link ( scroll down the pages for individual links) -
includes a detailed link to Jungfraujoch information -
as well as other mountain tops throughout Switzerland.
The Niesen is included, within reach from Wengen:
Further afield, and in that list, but at least possible, are Gornergrat and/or Klein Matterhorn at Zermatt, which would be a long day trip.
And, there are a variety of ascents that go to quit scenic alpine locations with actually going to the top ( in German "der Kulm"). Their availability often depends on the time of year.
<<"in the Wengen area">>
The availability of excellent train connections throughout Switzerland from Interlaken makes the answer to that question somewhat elastic.
One definition might be the Bernese Oberland:
or, closer to Wengen:
and, specifically, the Jungfrau Region:
You can use the Swiss Rail ( SBB) timetable to help define your limits. This page provides valuable, probably necessary, tips for using the website:
Once there , you can download a free SBB app for your smartphone that will be valuable.
And, a map certainly helps. Many are suitable, but I like this one in particular because of the way that it makes the train lines really stand out as you zoom in. The menus are useful, too:
Zooming in to the Jungfrau region, and adding train and mountain transport stops from the menus is helpful:
Mouse over an icon to get the exact name of the transport stop for use in the timetable.
You can also add bus and tram stops from the menus:
which lets you see the bus route along the floor of the Lauterbrunnen Valley, as well as the local buses at Grindelwald.