I would do it seperately with a good handwashing in between.
Better safe than sorry.
You shouldn't hold the cham much so you shouldn't have to worry about this too often.
I'm not sure if this counts as handling or not, but every time I open her cage to do ANYTHING she always grabs my hand, goes up my arm, and sits, as happy as can be on my shoulder until I finally have to put her back. I love her soooooo much!
Oh man i envy you lol i wish my cham did that but i guess, each one has a different personality. Mine just runs to the back of the cage and puffs up like he is huge and lol and he is only 4 months old.