Well, no one else seems to be chiming in, so I'll take a stab. I haven't been to Belize, so this is just generally speaking, since Belize is in the general category of Mexican, Carribean, and south American sort of locale. There are scores of various beach destinations all throughout these locales, of course, that Americans travel to all the time. Thus the question comes up over and over on forums, for all the different islands and/or little independant countries down there.
Basically, you might get a "no", if you kept asking long enough (for example, talking to consulates, lawyers down there, border guards, travel agents, bureaucrats, etc...).
For example, this question came up, for Mexico in general, years ago, in a periodical that Fisher Co. used to put out, back in the 1980s. Someone had written in to the Q&A column of their periodical, asking if metal detecting was legal in Mexico (apparently they were getting ready to go to one of the tourist beaches down there). Fishers answer to them, in this Q&A column, was "no", and went on to elaborate the laws, etc.... In the following edition, several other readers had written in to take exception to Fishers answer to the earlier inquiry. They were asking things like "Since when?" and "who told you this?" and "we've gone down for years, and never had a problem, so where are you getting this info?" etc.... Fisher defended their answer by expanding on their earlier answer: In order to answer the earlier inquiry, they had simply gone to some border consulate bureaucrat, or lawyer or whatever ........... AND ASKED! Doh. Seems logical enough, right? I mean .... who better to ask, than Mexico themselves, right?
But of course, whomever fielded their question, probably couched the answer in terms of Shipwreck salvor laws, export laws, federal historical monument type stuff (ie.: raiding the pyramaids, etc...). So too might the same answer be given to you, if you asked long enough, and hard enough, at a lot of USA sites too. Why is this? Because perhaps the bureaucrat is thinking of Shiloh, Gettysburg, Mel Fisher legal hassles, or that you're going to be a moron and leave holes, etc....
And using that example of Mexico, detectors are a common site on tourist beaches, despite any answer that Fisher might have gotten. And there are detector dealers in all the major cities of Mexico (including Fisher dealers! Doh!), who presumably sell them to people who are going to use them. So the answer made no sense.
This is the same thing I would be afraid of in any other Mexican, Carribean, or S. American place: You may get a technical answer, when in fact, no one really cares. A lot of people who got "no's" (when they asked their cruize line, or travel agent, or whomever), have been surprised to see others on the beach once they got there, having no trouble at all.
The same pyschology is seen on a micro-scale here in the USA: A lot of parks (for example) are detected with no problem for as long as anyone can remember (it never occured to anyone there might be a problem, or that you even needed to ask). But then someone takes it upon themselves to waltz into city hall, and ask permission. They get a "no". What's up with that? So it's the same thing ...... a lot of times ...... on a national scale too I suppose.
If you are still skittish, you might look to see what dealers are close by (Whites, Fisher, Garrett, etc... all have lists of their international dealers on their websites), and contact the dealers who are close (even if not exacty right in that particular country/state). See what the real skinny is.