Annika has given an excellent perspective on your two possible itineraries, and, the pluses and minuses.
She has noted the timetable, which is really your friend on either itinerary:
Unfortunately, the weather will be unpredictable in the Alps until only a short time before it happens; you have noted that point as well.
One possible approach might be to head to Luzern upon arrival, then on the morning of the 19th, consult the tourist office in Luzern by track #1 in the main station; also use the internet -
and Swiss TV 0n channel 1 ( weather forecasts in the early AM as well as web cams.
Then choose whether to stay in Luzern or head to the Bernese Oberland for a stay or a (long) day trip.
If you stay in Luzern, a lake boat ride and the cograil up to the Rigi from Vitznau could be pleasant; also weather dependent.
The lake boat service in the winter is limited, but there are a few trips each day that run the length of the lake ( to Flüelen) and back, stopping at Vitznau as well as other stops.
I have not visited the Alps in February, so I don't know the availability of rooms on short notice. Arno and Annika have a much better perspective than I. My limited experience suggests that rooms will be available in Luzern on short notice in February.
I think that Bern would be my choice.
Annika's suggestion to stay in Bern makes good sense for a flexible base- the trip to the Bernese Oberland is shorter (though less scenic) than the trip from Luzern. Luzern is as little as one hour from Bern and makes a nice day trip; see the attached screen grab from the SBB timetable.
The arcaded streets in Bern are nice to walk in the Winter. One picture attached is from warmer days. There are no roses in the Rose Garden, but the view of the city from up there is nice. (Attached).
Staying in the mountain villages ( Wengen, Mürren) is wonderful, if you can see around the mountains. Much less attarctive, but still a nice experience, in cloudy weather.
Personally, I like Wengen: