welcome to fishlore!
if the fishbowl isn't cycled, it should be alright to transfer him (along with any substrata, decorations, filter media, etc) to the 10g. I'd recommend finding a product called Prime at your
LFS to treat the tap water with. One of those empty plastic travel squeeze bottles for shampoo, etc at a store like walmart is a great way to measure it out by drops - we do 1 drop per gallon.
check this link if you've not already:
http://www.fishlore.com/NitrogenCycle.htm for more info on the cycling.
do you have a heater for him? they like the water around 78-82.. although i think you're heading into warmer weather now so i don't know how much of an issue a heater would be.