Yes, 80-100PSI air and a very low water amount will make a very cold mist just wet enough to lubricate and cool without throwing water everywhere. In getting it fine-tuned, start with 90PSI and them adjust the water from off until the mist is spraying. Increase it until it is a bit wet, then back it off until it is just right. You don't need much pressure on the water. A small pump is fine, and even gravity feed will even work.
I use the same type of water supply as my chiller platen. It is a Polar Cube. It is portable, has its own pump, container, hoses and connectors, and holds enough kool-mist mix for a good long grinding session.
It is also superb when filled with ice and water and used on the chiller platen. The recirculating water in that setup will stay cold for a couple hours grinding time.
Many folks who have had joint surgery are given one for free to take home. They will probably give it to you when they don't need it anymore.
They are several hundred dollars new but sell for $25-$50 used.
They are dirt cheap on eBay and such places and can often be found at yard sales and estate sales even cheaper. I paid $10 for one at a yard sale and got two free when I had a shoulder surgery and a knee surgery.
Kool-mist can be used on other equipment, like a drill press, bandsaw, or milling machine to keep heat down. Most of the units have a magnetic base that makes moving to a different machine easy. A plus is they blast away the chips and swarf. With a Kool-mist, you can usually increase cutting speeds and feed rate.
Again, the Kool-mist lubricant concentrate is well worth the price. A $55 gallon will last most knifemakers a year (or more) at a 32:1 mix rate. It has algicides and rust inhibitors in it as well as a lubricant. The fog is harmless and completely non-toxic.
I haven't done it but have read where folks take a piece of heavy plastic sheet and attach magnets on one edge. They use it on the drill press, milling machine, or grinder to control the fog/mist or spray from flood cooling. It keeps the cleanup in a controlled area. I suspect a U-shape bar of metal placed over/around the machine would be a good attachment for the magnets. Other magnets or bars of metal can hold down the bottom edges of the sheet.