Seriously I think the above answers are good. I'd be careful not to spray the leaves. It's very cool looking I like it the client has good taste in groomers & gifts.
Spraying with a mister should work just fine or tip the container, dribble a bit of water down the side, just don't soak the medium especially this time of year. I have a lot of succulents in the greenhouse sitting on cafeteria trays, in the spring and summer they just get hit with a watering wand. In the winter they get a bit of water maybe every couple of months but bottom watered if I see the leaves of any of them starting to look a little limp.
The thing is when the leaves are wet keep it out of the sun as water droplets act like a magnifying glass and those spots could burn.
By the way, gorgeous bowl of succulents, lucky you.
Annette
I thaught that the plants were in a clay pot, not glass. In that case you may want to go to a glass or a shower inclosure business where they use a diamond bit.
An eye dropper might work better then a mister. You won't have to clean the sides of the bowl. Any way you can get a small amount of water into the bowl will work. The display should last a long time with no tending other then the occasional (rare) dribble of water.
I think it's lovely. Your friends and clients know you well.