how can i (physically) clean a deck of cards??

my mom gave me her tarot deck, shes had it since she was a kid and its very grimy, after shuffling with it for a while i had to clean my hands. this is my first tarot deck ever, so im so nervous about doing something wrong.

can i just wipe them down with huggies, and put some cornstarch on them? is that safe? im so scared i will ruin them or give them a bad texture, please help