Can anyone recommend a heart rate monitor (watch) that can use a non-coded transmitter? I have a non-coded strap laying around and need a cheap monitor. Thanks much

Um. It's not gonna work unless you have the watch brand it came with. Un-coded means un-standardized which means un-interchangeable.

Not necessarily so. I have used No Name, Ciclosport uncoded and sigma uncoded straps with my uncoded TACX Fortuis trainer. Never tried an uncoded belt that didn't work.

Yeah, I originally bought this non-coded Sigma transmitter to work with other heart rate monitors. I was under the impression that it just wouldn't work with a coded monitor... as long as the monitor is non-coded, then it should work.

As others have said, they all work IME. I've got a couple of really cheep ones and a polar one. They all talk to each other and to the equipment at the gym. The only one that they dont work with is concept2 rowers which for some reason went against what everyone else had done and use ant+.

As for the original question, I've not seen a standalone cheep 'watch'. My polar F7 was about £25, and my mum's got one from Tesco which works just as well, but both came with belts.

Let me rephrase my response.
They won't always work, and there will be no way of knowing ahead of time. This is a moot discussion though, because un-coded HRM's are always el cheapo (<$30) and always include the belt anyway. So if you're looking for a $10 watch without belt, then just find someone on e-bay selling the watch without the belt.
Un-coded just means that the heart rate signal is directly modulated on an RF frequency and then demodulated by the receiver, without any sort of encoding scheme to prevent interference. The signal power and RF frequency between manufacturers can differ which would make them not work. Since 99.9% of them will probably operate at unlicensed frequencies of 900Mhz or 2.4Ghz odds may be pretty good that they'll work.