As long as the tool can tolerate moisture water don't worry about it, you can even water cool it as long as the tool has drainage, then just let the foam dry for a while. It is closed cell won't absorb water, just a tiny bit in the cells that get smashed, but easy to dry out. Also foam manufacturers recommend storing the foam after any kind of processing for a while, or at least not glass it immediately after cutting, even the non outgassing foams do outgass a tiny fraction from smashed cells due to cutting, heating or storing the foam for a while takes care of this issue. Same thing goes to sanding it - don't glass immediately after sanding, from what I've read corecell is one of the most stable regarding outgassing - being advertised as non outgassing foam (the SAN one), but PVC's do have some outgassing going on from processing like cutting and sanding. Baltek has very specific info for their Airex foam and issues with processing&outgassing - the C70 Airex.

If you will be cutting a LOT of foam I think the best approach would be to build a dedicated tool for it with very thin blade and indeed smaller diam. Long bed to accomodate sheet, solide fence, fingerboard, a jig to keep pressure on the foam to keep it on the table - and cooling of the blade - but only for lots of cuts of course. A smaller diameter disc will require lots of rpms but not much power for foam, ideal motor for this will be an RC motor running on 24V , they have speed controllers, at 24V you will get about 25-40000rpm from common rc motors, plenty of amperage and torque for cutting just foam.
This is just ideeas, don't get me wrong, it is always best to manage with the tools at hand. But if I had to (for example) cut foam for a 30' trimaran I would have a dedicated tool for foam cutting. Cutting foam with a 12" blade tungsten carbide teeth is like carrying groceries with a 40ton truck IMHO.
Anyway best of luck with your project and don't be shy on posting pics.

regards