1) A box cutter does one thing, very safely and well--cut open boxes, but is less useful in other situations. I don't know how often you have to do that, but for me, at most, it is only a couple of times a week; unless you are doing it several times a day, a single use thing for EDC seems a bit of a waste. Better to carry something that will do that job AND do other things, even if only as a "backup" to other things you may EDC. So, for me, a single task item is less useful than something that is a multi-tasker.

2) The SAK has a large blade and a smaller blade; it gives some of the same flexibility as the box cutter that has different depths.

3) the blades of the SAK are relatively easy to sharpen.

4) it has other tools that I actually have used: can opener, bottle opener, large flat screw driver, Philips head screw driver, and the one that has helped me so many times, the very small flat screw driver on the tip of the can opener that fits the screws on my wire rim glasses that keep getting loose and the lens pops out) (I find it useful to be able to see). I don't totally understand your needs, but having these things available as part of your EDC may be very helpful, as they have been for me.

5) Downside is that it does not lock. I have never found this to be a problem, and in opening boxes, since the force you will exert is only in one direction, I don't think this is a critical issue.

It will do everything that I understand that you need to do, and so many potential and actual uses, IMO spending money on a dedicated box opener seems a waste when you can do what I understand that you need to do and have so much flexibility to do other things as an addition to your preps for a very reasonable cost---less than what you were originally thinking of.