Explicitly mentioning “no cameras” is currently very off-putting because the expectation is that there are no cameras in private accommodations. It comes off as well as saying “We won’t file a frivolous damage claim against you.” That wasn’t something I was really worrying about, but, well, now I am.
There is one exception, and that is to clarify both where the cameras are and aren’t. Saying “We have a security camera over the garage door, but no cameras in the house” comes off much more sincerely.