Train 2 or 3 Country

Yes, if you have a two country pass, you can just buy tickets for the uncovered portions.

Before you buy a pass, though, post exactly where you'll be going in Switzerland and Austria (or as much of it as you're sure of). You can often get a better deal by buying a pass just for Switzerland, which covers more than the two country passes do, and then buying advance purchase discounted tickets for Austria and Germany.

Also, before you buy any pass, make sure you read this article and understand all its points thoroughly: https://www.seat61.com/Railpass-and-Eurail-pass-guide.htm#railpass-or-point-to-point-tickets

Will I be able to use a pass from Hallstatt and simply pay the short German portion to Fussen?

The "short" German portion to Fussen (Salzburg to Füssen) is actually about 4 hours long (via Munich). If you don't mind doing the trip with regional transport, the trip from Salzburg to Füssen can be done using a 25€ Bayern-Ticket. You would need another Bayern-Ticket to get from Füssen to Innsbruck, or from Füssen to the Austrian border at Bregenz, where you could use the Austrian pass again.

So, about $60 in fares plus the extra for a third country.

What is your overall itinerary?

Going Hallstatt --> Füssen --> Switzerland is a very inefficient route. The problem is the Alps, Füssen is on the north side (the Austrian border follows the ridge behind Füssen).
The quickest route is Hallstatt --> Salzburg --> Innsbruck --> Switzerland. This doesn't look far from Füssen on the map, but is difficult because of the mountains. The rail line at Füssen runs north to Munich, not south to Innsbruck. You would have to go Salzburg --> Munich --> Füssen --> Lindau --> Switzerland, a much longer route with much changing of trains.

If you skip Füssen, and go Hallstatt --> Salzburg --> Innsbruck --> Switzerland, you then only need a 2-country pass.

I would also cost out buying advance tickets for Austria and a Swiss Pass (or a Swiss Half Price card) for Switzerland. That may be a cheaper option.

Current plans are: 3 days Vienna
3 days Salzburg
2 days Hallstatt
2 days Fussen
3 days Appenzell
3 days Zermatt
4 days Murren
1 day Zürich.

Your Austrian travel plans absolutely do not require a travel pass as that will be a total waste of money.

Vienna to Salzburg - 19 Euro on OeBB.at purchased online in advance or 18 Euro on Westbahn.at.

Salzburg to Hallstatt - buy an Einfach-Raus ticket for 34 Euro for two people (17 Euro per person).

Hallstatt to Füssen - fares and schedules on OeBB.at.

Thanks for your help everyone.