You say you are interested in the relationship between two variables, so the quantity you want to assess is something that describes that relationship. Usually that is the regression slope.
A much more serious problem is: how are you going to generate random permutations that honor the spatial correlation implicit in a SAR model? You can not simply permute X variables, Y variables, or residuals because permutation assumes exchangability, a slightly more general version of independence. You might consider toroidal rotations, but that makes other assumptions (e.g. 1st order stationarity) Pesarin has been developing permutation tests for complex data (see his book with that title). I do not know whether he has considered data with a SAR structure.