How to determine wheel size on touring bike
The gear system doesn't play into the rear tire sizing. 

Assuming your old tires are 26x2.0 (not 36x2.0), your rim is an ISO 559 rim and you can buy any tire marketed as 26 x some number in decimal. 

That being said, the size of the tire you can run in practice is determined by frame clearance (not a problem since you're going to a smaller tire) and the rim width. If the tire is too narrow for the rim, increased likelihood for rim damage from road hazards. If the tire is too wide, you may have reduced control. But the tire will physically go on a rim thats too wide/narrow if its of the right diameter (in this case, 26 x something in decimals or a tire thats marked as ISO 559). 

That being said, most likely you are fine with running a 26x1.75 on these rims.