Is that the digital probe, or the analog dial? The dials are incredibly inaccurate: I've had them read up to 60% higher than my digital probe hygrometer!
You could definitely make a dripper until your new one arrives: a few small holes in a pop bottle will work fine, just make sure to leave the top off or poke a hole in it too or else it will quickly stop working. Your cham may be too shy to drink as much as he need in front of you as many chams are shy drinkers. A dripper will allow him to drink while you are not there staring at him

Make sure you are using warm water: most chams hate cold dripper or misting water.
You could also try the shower method: put a plant (real with well-draining soil, or fake) that he can comfortably grip into your tub and run your shower head on warm- not hot! The shower stream should hit your shower fall, so only a fine mist falls on the leaves of the plant your chameleon is on. Place your chameleon onto the plant. You can leave him there for 30-40 minutes, checking on him frequently to make sure he's still okay. I bought my silk "shower free" from Ikea for $25.
A fecal check for parasites is also a good idea.
A few notes on that enclosure:
- The waterbowl is basically worse than useless: they will often just poop in it, and even if they did drink from it (which they generally will not) by that point it would be pretty fouled with bacteria, etc. I'd just take it out as it only offers a false sense of security.
- I'd also take out all that substrate. Chameleons are notorious for eating it, which can definitely cause an impaction or blockage. Also, it tends to get waterlogged and mold, what with the amount of water that you have to run through it for a cham unless you have an additional drainage layer and some kind of collection/disposal system beneath. The vast majority of people here use a bare bottom, and just wipe up any feces or water spots with a papertowel, etc.
- And, honestly, he could probably use more foliage and branches. You want their enclosure (hopefully at least 24"x24"x48") stuffed FULL of leaves and vines and (mostly horizontal) branches. You really shouldn't be able to see your cham most of the time! When you think: "That is too much foliage", it's probably just right.
