Yup, I used another empty critter keeper or deli cup to hold mine in when cleaning, you don't want to set him anywhere loose.
Pretty fast little scuttle butts. I had an incident that was almost bad, was sitting on floor and he jumped and zoomed off, I was able to leap over and cup my hand over him before my cat got there (cat was on it!). That was really scary as I hadn't expected the gecko to take off like that. What I started doing was taking him out in the bathroom and sitting in the tub, letting him jump and crawl all over me, to start gaining trust and so I could learn myself how they moved. (covered the drain of course) (I ended up donating mine to my herp society for a benefit for USARK a few years back). They are awesome geckos.