Hi there
I use a hair hygrometer like this one although the one I got was maybe a bit more expensive than this one (which is £10)
http://www.thermometerspecialist.co....er-7cm-44-2000
There are also digital ones which don't cost much but I think they are not as accurate as the ones that don't use batteries.
I think it's handy to have one but if you use a plastic container over a damp substrate then it's definitely going to have higher humidity than being out in the open area so maybe a hygrometer is not really necessary.
Other plastic things that I've used for hides are an upturned seed tray with a hole cut in it and an upside down plant pot. With the plant pot I found I could press it down into the substrate so that when I put a weight on the top as well it was truly fixed to the spot. The seed tray worked well and it can't be tipped over even without a weight on the top.
I know just what you mean about the risk of something going wrong when we're not there to notice and put it right. With the seed tray the tortoises sometimes did climb up on during the daytime but this wasn't causing a risk in the enclosure.