Hey I actually found what I was looking for so I thought I'd check back... Thanks for all the helpful suggestions, though! I was at Petco and I found this stuff called Pet Party Printz, it's a wrapping paper that is non-toxic and pet safe, and it even comes with a special adhesive that is pet safe as well... I hadn't even thought about the glues in tape being a risk... You're probably right about the other stuff, but this stuff is only $5 so why risk it? Thanks everyone!
Edit: They have a website as well, you can google it if you're interested.