Amy's got good questions - can you update us on how he's behaving?
I've just now checked spreadsheets for 3 cats that are OTJ and I don't see any numbers below 50 and only one in the 50's. That doesn't say that it couldn't be ok, but at least on those there isn't anything that low. A while ago, I checked a friend's cat locally that was in the low 40's - not diabetic but they were concerned. I also just looked at punkin's lab tab on the ss, and it shows the normal glucose reference range as 70-150 but that would be using an AT equivalent. I suspect that would be equivalent to something over 40 on a human glucometer.
That seems pretty low to me, and although we typically don't think of a cat not getting insulin as being able to become hypoglycemic, there are some unusual medical conditions that can cause low blood sugar. We used to have a member whose cat had a special condition and the cat did have a hypo while not on insulin. I think i'd give a call to your vet, but make sure before they panic at the 34, that you remind them it's on a human glucometer. If you still have good strips on your AT you might test with that first.