Here's a study that shows a picture of the hand held device which is most likely hooked up to any DC current device such as you are currently using. The "dry ionto" isn't exactly dry. Ionto requires water.
The "dry ionto" works the same as water ionto except instead of water it works by your sweating hands. The hand held device is simple enough to build. The drawback is suppose your hands aren't sweating at the time of treatment?
Three simple solutions for your water spillage problem.
1) Smaller trays using less water.
2) Smaller trays, less water while wearing cotton gloves. The gloves will wick up the water and cover more hand and finger surface area.
3) Smaller trays with sponges in the water. Your hand goes on top of the sponge. Make sure you are using sponges that are not too firm.
Article:
http://www.sweathelp.org/pdf/Dry_Iontophoresis _Na.pdf