Switzerland Itinerary

If you have a morning to early (or even later) afternoon arrival, it is perfectly fine to press on at arrival, Swiss train travel is so easy there is no reason not to.
However, if you are still refining, I would eliminate Zermatt. I can’t imagine anything that would compare with the Bernese Oberland, especially for first timers, plus it is so weather dependent. Then you could add a night to Wengen and definitely add one to Venice and Rome. Then I don’t think even the most picky among us could find any fault with your itinerary!

I think it makes sense to take a train to your first destination on the day you arrive. We often do that.

I don't know Switzerland well enough to comment on that part of your itinerary. But if you do not follow the advice to delete Zermatt and redistribute the days to Wengen, Venice, and Rome, I would delete Venice. I love Venice but you will spend a good part of the day traveling from Lake Como (two trains at least) for a very short stay. You have the same stay planned for Rome so I would give those days to Rome, since you are flying out of Rome. If you have been to Rome and it is only a stop before your flight home, then you could give one day to Venice (3 nights Venice, 1 night Rome). But in my mind, two nights is not even beginning to do justice to those two cities. You would be better off seeing only one of them.

Re: going to Wengen on arrival. Just pointing out that since you arrive in the AM, you wouldn't be able to check into a hotel anyway, so continuing moving forward for another couple of hours makes sense.

Going on to Interlaken on your arrival day makes some sense... but the next morning the Interlake to Wengen leg will be very short so you will still have the check-in issue. Zurich to Wengen is only about 3 hours - getting you in before check-in too. Maybe check out SBB.ch the Swiss rail site and the Trenitalia.com to sort out travel times among your proposed stops.

After many trips to Switzerland agree with going to Wengen on first day and possibly eliminate Zermatt and Venice and add the Dolomites which are amazing…too many stops are taxing on your travel body🙂

Is it a bad idea to go to Interlaken on the day we arrive?

Not at all. As was mentioned above, you arrive in the morning so you have the entire day before you. Yes, you will be tired and might fall asleep on the train, just make sure you have your important items right with you in some way (when I took a night train once I just slept on my purse). If it is important to you to try and stay awake, you can move around, go to the restaurant car, or perhaps even take turns having a short nap while the others remain awake.

What is nice is that Interlaken is the end of the line, and of course you can set an alarm on your phone or whatever as well, so you won’t miss your stop. During the transfer to Wengen you will likely wake up enough to carry on - and even enjoy the scenery along the way. 

Train Zürich Flughafen - Wengen is around 3 hours. There is a direct train to Interlaken, with no changes, leaving at :46 after the hour, if it works with your timing you can take that one for ease of travel.

I personally think that you should not give up Zermatt. You have already cut out Luzern and in the end your only Swiss destination would be Wengen. One thing that I think is wonderful about Switzerland is that even though it is an extremely small country, there is so much variety between locations. Zermatt is so very different from Wengen and I think that they are both worth visiting.

It is not a big deal to get to Wengen your first day. There is a direct train to Interlaken from the Zurich airport and then you just make a connection through Lauterbrunnen up to Wengen. You'll have all afternoon to relax with beautiful views, take in the area, stop at the grocery store and be tired in a beautiful place.

Personally if your group isn't in to cities, I'd remove Venice and spend some more time in the mountains. I think 5 bases for 18 nights is plenty. Your first couple days will be pretty heavily jet lagged and you may find you need to sleep in a bit. I'd take those 2 nights in Venice and add them to the mountains for jet lag & weather buffer, which you'll need. There is SO much to do and see from Wengen as a base, including lakes, castles, mountain viewpoints, hiking, biking, valleys, waterfalls & adventure activities. You won't run out of variety. If Venice (and all the stops you have) is a must, then perhaps take a nice away from Zermatt & Tuscany and add it to Wengen. I'd atleast do a minimum of 5 nights there. Zermatt really only needs 2 nights. It doesn't have near the variety as Wengen and you can easily get what you need out of it in 2 nights. Having longer in one base to start the trip will be worthwhile so you're rested for the go, go, go of covering so much ground.

Wengen 6 nights > Zermatt 3 nights > Lake Como 3 nights > Tuscany 4 nights > Rome 2 nights
or
Wengen 6 nights > Zermatt 2 nights > Lake Como 3 nights > Venice 2 nights > Tuscany 3 nights > Rome 2 nights