What is the difference in dehydration of cis- and trans-1,2-cyclohexanedicarboxylic acid in anhydride formation?
The mechanism of formation of anhydride from a dicarboxylic acid is as follows: [1]

So as you can see, it involves a nucleophilic attack at the $\ce{C=O}$ of one of the carboxylic acids by the other one, following which internal rearrangement occurs and a water molecule is kicked out.
Stereo chemically, we are interested in finding out in which configuration can the lone pairs of oxygen from one of the $\ce{-COOH}$ attack the $\ce{π^* C=O}$ type antibonding orbital of the other $\ce{-COOH}$ group.
To achieve this, the nucleophile( oxygen in this case) has to align properly with the $\ce{π^*}$ orbital at the Bürgi–Dunitz angle. This configuration is necessary whenever a nucleophile has to successfully add to a carbonyl group. The interacting diagram will look like this for formaldehyde: [2]

(Green ball= nucleophile| Blue and Red balls= carbonyl)
We can also roughly estimate that the situation will be similar for the $\ce{C=O}$ part of the carboxylic acid group.
To see which of the two reactants in question will form the required anhydride, one can simply look at the 3-D conformers of both in the appropriate orientation, and compare to see which of the cases resembles the standard Burgi-Dunitz interaction more closely as illustrated above
Here is the cis configuration: [3]

And this is the trans configuration: [4]

1= oxygen| 2= carbonyl of acid group
As you can see, the oxygen seems much more aligned with the carbonyl in the trans configuration as compared to the cis. So, 2 might form the anhydride more easily than 1 (that is, with a lower activation energy barrier due to reduced torsional strain)
But again, it's not a strictly inaccesible barrier, as a few bond rotations in the cis configuration can also lead to a somewhat favorable configuration for the reaction. So it may ultimately lead to two different kinds of anydrides by each of the isomers like you said, 2 can lead to formation of 4, while 1 can lead to formation of 3