The burning of any common fuel does indeed produce water, which is about the last thing wanted in sealed storage.
Common fuels are all mixtures or compounds of hydrogen and carbon, when burnt they produce water and carbon dioxide.

Chemical hand warmers come in various types, some slowly burn small amounts of lighter fuel or charcoal, these would not be suitable.
Other types contain iron powder in a sealed pouch or other container. These should be suitable, they react iron with oxygen to produce iron oxide, no water is produced.
Iron oxide can be corrosive in the long term, I would be inclined to place the handwarmer in a peforated rigid plastic container in order that it may not contact the stored goods.

One drawback of any oxygen absorber is that the removing of the oxygen from the air in the container reduces the volume of the air by about 20%.
This causes stress on the walls and lid of the container and in the long term may lead to cracks, fractures, leaks or distortion.
It might be worth briefly and slightly opening the container after a few days in order to eqaulise the pressures. This will of course admit more air containing more oxygen, but a large enough oxygen absorber should absorb this as well as the first lot.
After the second and final sealing of the container, the pressure within will again drop as the oxygen is absorbed, but this time by only about 4% rather than by about 20%.
The effects of this may be minimised by finally sealing the container on a very cold day, or after storage in a refrigerator.