I think you can say: for "Hold on a second, please" chotto matte kudasai or (more polite) chotto matte itadakemasenka for "Let me think", I'm not sure, but you could say: eeto ima kangaete imasu (ehm now I'm thinking)

We have several ways to say "hold on a second" for politeness. Normally we say "chotto matte kudasai" or "chotto matte" in our daily conversations. The politer ways to say it are "sukoshi omachi kudasai" and "shoushou omachi kudasai" and we use them in the formal situations. The direct translations of "let me think" is "kangae sasete (kudasai)" and sometimes we say so when we need time for thinking. The other translations are "soudesune..." or "eeto..." like "let me see..." and they are used when we say/ answer something but now we are thinking how to say/ answer. Espero que te ayude. ^^

I wonder also :o hmm, all I know is "chotto" xD