Additional issues are likely to be clearance for getting a CX tyre past road callipers and limits imposed by rear stays.
I’d recommend borrowing a set of wheels and offering them up or spending some quality time with a ruler.
FWIW the Alex 430’s on my weekday build X with 700×33 Raze’s have survived a year of the worst conditions Sheffield’s beautiful roads around Attercliffe/Brightside can throw at them as well as big chunks of the Dark Peak that look very much like real mountain bike territory… They’re heavy wheels but bulletproof and still true after 18 put the back wheel together properly for me (very loose spokes at a month old). I tend to run around 60F/80R for town and 40F/60R off road or thereabouts. Sometimes more or less. I’m seriously contemplating some XT 29er wheels as a second, lighter set. I’ve really surprised myself at how many times I’ve left the mountain bikes at home in favour of the X this last year. Shame they’ve dropped it. Disc brakes are a massive win for all weather cycling, with the additional bonus of not leaving you with a rubbing brake after bending a wheel should the worst happen.
Is C2W an option? Plenty of capable CX bikes under the magic grand…