In short, it's an extremely complex answer. We think of Switzerland as a single nation now, due to its tremendous relative success in forging various cantons and ethnic nationalities into a single national identity, but that is not how things started, in fact the vast majority of Switzerland were separate rebellions or states that joined in Confederation after the fact. Others have already mentioned the Grey League and the more peripheral areas of Switzerland, but even what we consider core Switzerland was not actually united at the start with the rest.
Are we talking about making sure none of these worked, leaving all these territories eventually under different nations' control, or just that they never unite?
The original Old Confederacy is the three Forest Cantons: Uri, Schwyz, and Unterwalden who originally formed the Confederation in a war against the Hapsburgs, but were already reichsfrei in the first half of the 11th century, with the city states of Bern and Zurich being independent reichsfrei even earlier at 1218 with the death of the last Zahringen. Uri, Schwyz, and Unterwalden had a lot of important treaties and pacts due to their close proximity and need to defend themselves.
The initial popular conception of an independence war never actually existed. As stated, the Forest Cantons and Berne were already independent of the Hapsburgs (Zurich technically was too, but was invaded and made to acknowledge the Hapsburgs as "patrons"), except when Albert was on the Imperial throne. What the real war was about was the threat of possibly losing that status in the future, but even that wasn't guaranteed. It was motivated by fear of lost trade after the Hapsburgs bought the rights to the town of Lucerne, endangering the trade via the lake to the Forest Cantons, and it was actually just a tiny part of the bigger war over the Imperial throne.
Assuming the big issue of the OP is no independent Switzerland there are a few scenarios.
Scenario 1 - Hapsburgs Win Morgarten: This involves the Hapsburgs being somehow tipped off or not suffering a rout at the eponymous battle. They win, by whatever margin, and force Schwyz and Uri to acknowledge their dominion of the Gotthard Pass, though the fact that Unterwalden's troops did not participate and are still fresh and ready likely causes the Hapsburgs to stick with their small gains for the time being. More importantly, this requires the Hapsburgs win the Imperial battle as well, or their victory will likely be ignored and set the stage for new battle. From here on out, the Austrians have embroiled themselves in a perpetual low-level battle for influence with periodic flare-ups. The Everlasting League endures for however long, losing influence more and more as the Hapsburgs establish themselves. As the HRE ruler is likely to switch between them and other houses at least a few times, the League will come back, backed or aided by other powers in other theaters. It takes a lot of luck and skill for the Hapsburgs to continually win, but whether they do or not, we've limited the influence of the Forest Cantons until they're just one more part of the wider HRE. If and when a united Empire or Germany develops, they will just be one more arrangement in figuring out that government. The more Hapsburg control is granted, the more other powers are inclined to support the locals against them, either forcing a final conquest or a different independence. There's just too much grey area and speculation here without more guidance.
Scenario 2 - Expansion is stopped: There's a couple ways to do this, so I won't detail them all. Suffice to say, a lot of the Swiss Confederacy's growth in territory was related to luck and distraction of larger powers with more important issues, as well as defeating their own internal secessionists. Assuming that they lose some more of those wars or that the Old Zurich War goes badly, you lose a larger part of Switzerland. The less of Switzerland there is, the less power behind them, the less likely they will be able to establish effective independence from Imperial Laws and, de facto, the Empire. Again, Switzerland is just a small portion of the Empire, though may be more influential than other regions. See previous scenario regarding effects.
Scenario 3 - Switzerland loses the Swabian War: This is the simplest in terms of what it would result in without speculation, but also difficult in how to do it. I'm not overstating when I say that this war was the Swiss's to lose. They were more numerous on the ground, their enemies were divided and fractitous, after the Burgundian Wars they had the experience to beat back any foes on their home turf, and above all else the Milanese really pushed hard to end the war quickly so they could hire Swiss mercenaries and get the political aid of the Empire against French invasion. The Swabian League needs to be a lot more gung-ho for Hapsburg Imperial authority for this to get off the ground. Assuming the Swabians and the Hapsburgs win, this prevents the Swiss from uniting with the Three Leagues of Grisons down the lines (maybe?) and the Peace of Basel, meaning that the Swiss are acknowledged as part of the Empire, with the responsibilities of taxes and obedience of Imperial laws rather than effectively being acknowledged as a separate political entity as in OTL. This leaves a powerful Alpine block in Imperial/German politics, that, again, will have long-term effects on the political development of the Empire, but may prevent Switzerland from striking out on its own.
There you go. Three bare-bones scenarios.