All Things Zombie: Hospital 911 was the rulebook that made me realize I could play THW with counters on a mapboard instead of using miniatures, so I definitely believe you can play NUTS! using your mapboards. For inspiration, go you YouTube and search for "NUTS Wargame Tutorial" by TheWargamingAddict, as he demonstrates an earlier version of NUTS using a virtual mapboard, albeit using squares instead of hexes. I've even played out some encounters by sketching my map on regular notebook paper and just fudging movement distances rather than attempting actual measurements.
Normal movement is 8", so it's pretty easy to scale your maps on 3 levels: 1:1, 1:2, and 1:4 based on the map you're using. Starting with hexes:
1:1 = moving from hex to hex uses 1" of movement, so you can move 8 hexes in open terrain using normal movement
1:2 = moving from hex to hex uses 2" of movement, so you can move 4 hexes in open terrain using normal movement
1:4 = (I used this scale on a Combat Commander map once) moving from hex to hex uses 4" of movement, so you can move 2 hexes in open terrain using movement.
With difficult terrain such as buildings and woods, you can double the movement costs. Consistent with the way a lot of board wargame rules work, units can always move 1 hex, regardless of cost (except when considering impossible terrain such as crossing cliffs, etc.). Movement factors outside the 4" increments, such as the slower 6" movement of zombies in ATZ, mean I'll only move them one hex. I once tried this by allowing movement where the counter straddles 2 hexes to indicate the extra movement.
When playing at 1:2 and 1:4, I allow stacking so that multiple figures can occupy the same hex. At 1:2, I typically limit to 2 figures. At 1:4, I will use only one counter or marker to represent the entire group, and I'll list the members of the group on a separate index card or roster sheet to track each person's status. I've had several games that I've played on an Excel spreadsheet where I have one tab gridded as my map, and my roster listed on another tab (or even on the same worksheet below the map).
Square grids also work, as I prefer this method with urban environments. Orthogonal movement is treated as mentioned with hexes, but I use 1.5", 3", and 6" for diagonal movement at 1:1, 1:2, and 1:4 respectively.
You'll have to play around with this yourself to come up with something you find intuitive, but it can be done.