As far as same hardware 'twixt the n810 and n810w..purely a guess on my part considering I have never had a n810w ..that you are correct (?)..the only diff is the wimax (possibly?)...but I suggest reading alllll there is to read on the wimax edition....for clarity's sake.
If there is a lack of material I suggest contacting via pm maemoers who owned one in the past who were savvy and experimental ...perhaps they can clear up some of the fog for you.

To be cautious always use the correct firmware for the specific model.
Even if things seem to be fine with using something else...
It just avoids needless troubleshooting from something going haywire as a consequence of some unforeseen interaction.