At least a partial answer:
Raileurope and Wiki has told me that EC (EuroCity, formerly called Cisalpino, not all EC, just the former Cisalpino) and so called ICN (Intercity-Neigezug, German for Intercity Tilting Train) trains are tilt-enabled.
Using the Deutche Bahn Travel Service one can exclude EC and IC (InterCity) trains from the search by using the "Advanced selection of means of transport". Uncheck the EC/IC check box and search away, it should result in transportation without any tilting trains.
It should be noted that unchecking the IC check box should only be used on this route because there only ICN trains. Doing the same for Sweden would result in removing the non-tilting IC trains but not the tilting X2000 trains. But there is a way to solve this too.
When searching with All kinds of means of transportation you will see a "Products" column, it says IC, EC, IR, TGV or ICE depending on where you are searching. The EC trains on this route are easy to dismiss, but as mentioned above the InterCity trains cannot be dismissed as easily. But if you open the details for the IC trip in question it will say "Intercity Neigezug" (ICN) in the description if the train is a tilting InterCity train.
This method of course requires one to know if a certain train type is tilt or not. But it isn't that easy, because there are EC trains that don't tilt. And the ones that do don't have a special name like the ICN does. I have no good solution for this apart from doing a lot of research to find what kind of trains operate in a certain area.
Wiki has a list of trains with this feature, but I am not sure if it is up to date.
EDIT: To clarify, the IC trains in Europe are not tilt trains. Only the ICN trains. Some EC trains, such as on the route in question do tilt, but there are many EC trains in Europe that do not tilt.
Maybe the train company selling the tickets can also answer this question. It might be better to call the international ticket office, in my experience they have helpful travel and train fanatics that answer the phones. I've used this service with DB and SJ, if they didn't have an answer for my question they have been able to find out and contact me later.
Thanks to @Vince for pointing out that my answer could be misinterpreted.