Check to see if you're races are USAC sanctioned, and if you'd need a license. If so, they may have more specific rules, including tire width. If it's non-USAC you're probably ok on mtb tires, but check with the rules of the series.
Quite a few jrs around here race on mtbs, my kids always raced hardtails with flat bars.
I've had my best cx races on my 29er hardtail, I'm better at mtb (masters cat1) and do ok in masters cat1 cx. I've raced my hardtail in cx a few times, mostly when I know it's going to be a rough or more hilly (or a lot of sand and off-camber corners). I find the hardtail mtb is only at a disadvantage (for me) when we're racing on soft muddy sod, where the tires are sinking down into the muddy grass cutting a groove, displacing the mud, - the added drag from the wide tires made it about 5-8 places slower (not a whole lot, but noticeable, just a couple of minutes on an hour course). The other downside is it can be hard to pass the guys on the 17 pound bikes on the climbs, and I then get stuck behind them on the descents (where I'm a bit faster). A really sandy or rough course is going to favor the fat tires quite a bit. I've swapped in my carbon rigid fork, and it's about 2 pounds lighter but not really necessary for racing imo, if I were going to race the mtb on a smooth course I'd put the rigid fork on.
Unless your kid is a total beast and very competitive in cat1 open mtb, a 34 front on a 29er (I don't think you mentioned wheel size) would be more than adequately big, I run a 32 front on the 29er and it's plenty big. Even on a 26er, unless the courses are super smooth, a 34 front should be fine, he just might spin out on a paved descent. I'm certain most people new to cx imagine really hauling and carrying big speed, but the reality is you're grinding along on rough ground not very fast for 90% of it.
I always have a little more fun racing my mtb, but our courses are generally pretty rough. There's one especially rough course where a couple of cat1 open fast guys brought there fs bikes, they didn't smoke the field or anything, but I think they were less beatup the next day.