You're kinda screwed if he's an unusually large size. But guys that can just buy a watch and use the band it comes with are easy because adjustable bands adjust for a reason. Be it NATO style, steel links, whatever; only really big or really small wrists will be a problem usually.

So, the easiest way to get close is to use the very shirts he's likely to wear a fancy watch with: dress shirts. They'll be close to the size of his wrists, so you can button one up and measure the inner diameter. Just be aware that that is bigger than a watch band will fit, so that's going to be the upper range of length for the band and watch. If he also wears knit long sleeve shirts you can guesstimate the lower end by using those cuffs, though expect them to be equally approximate since they aren't fitted as well as even cheap dress shirts.

If the gift is a watch with a band already equipped, you aren't going to have to worry unless he's a weird size. But if you're getting a fancy band, be aware that wrist diameter isn't the only measurement needed. You'll need the width of the "lugs" which is the inner width of the prongs that poke out for the band to attach to in men's watches, 16-22 mm is the most common range. 16 is very narrow for most men, with 22 being as big as most casual wear watches should ever go, with 20 being maybe the ideal for 80%. But unless you get an adapter of some kind, it's not really possible to mix and match. You have to stay with the right lug size. The range only matters if you have to guess visually and want to hedge your bets.

You also have to factor in the watch itself. Most bands sold by length are only using the length of the band. So if his wrist is 8 inches around (unlikely, but that's the number at the end of the time on my screen), and the watch is 1.5 inches from lug to lug, you'll need a 6.5 inch long band (or one adjustable to that length). The exception to that is fabric bands that attach by running through the spring posts and under the watch, like NATO bands.