I have 4" holes in my canopy with 4" ducting going thru a window. I ordered the 6" fan & put a reducer from 4" to 6" coming into the fan.
Is there any problem with doing this?
I don't think with a fan in this situation you're going to have wear issues as you would if this were a water pump with a restricted intake. Instead it's all performance issues. Less area (^2 in.) in the intake opening will restrict the volume of air input....can't say by how much this may matter though.
Worse than that might be the restricted outlet though.
Did you have this
263cfm, 6" radon fan lying around or why not (if still possible) get one that's made for 4" ducts? They have the FR100 in the same series of fan you have, as well as others
like this one rated for 160cfm. 60cfm more than the FR-series. You aren't likely to get close to the rated flow with the I/O restrictions on yours anyway (but I wouldn't hesitate to call FanTech though and get their take since it's already in place) and the 4" fans appear to be a bit cheaper. If needed, you can add some additional CFM with
one or more 80cfm boosters like this ($14 online, $25 locally for me), which are way cheaper and add none of the bulk of a second main fan.
Anywho, if you can plumb the bottom and top cabinets into the 6" fan with something like
this, then you will maximize what you spent on that first duct fan by opening up the intake almost to +200% instead of -33%!

And if there's any way you can upgrade the window side to 6" - even if all else remained 4" - that would have to make a big improvement at least to get what you bargained for (cfm-wise) with the existing fan. I'm not finding the horizontally oriented part I'm looking for, but if you can catch my drift
something like this combined with
something like this, depending on the orientation of your window might do the trick? (I guess I don't know why the window side is restricted to 4" pipe, so maybe not. ;-) )
If you don't already have them, installing at least one vent opening in both cabinets for cold air return might not be a bad idea either. (If you find it necessary, small PC fans could be added to the cold air returns as well.) This would assure there's a good way for fresh, cool air to replace the hot air you are evacuating out via the duct fan, making sure the fan doesn't have to spend it's limited power on suction - just flow. You can see on the FanTech link how much your cfm's will drop due to restrictive pressure. (This is typical...any brand.)
Good luck!
-Matt
P.S. Another thought: Being less dense, the hot air will tend to "pool" at the top of your enclosure, so you might do some additional maximizing by tipping your ductwork elbow so it's "sucking" hot air off the "ceilings" of your canopy and cabinet. Kinda the upside down version of how
Reef Dynamics sucks the more-dense bubble-free water from the bottom of their skimmer body for the outlet.
P.P.S.
Overkill, but interestingâ„¢.