I don't think you'll have any problem keeping the cuttings alive on the flight. As long as they don't dry out, they should be fine. I wonder if you've considered the necessary PPIS permit though.

I think I won't have any problems with the PPIS. But is there anything special I should do to keep them alive longer other than keeping them between two damp paper towels?

No, the only thing you need to do is to place them between damp paper towels in a sealable plastic bag. They will stay alive for an extended period of time unless frozen or cooked by the heat.

Maxim, I have used the following method for years when transporting or shipping cuttings. I insert each cutting in a single white grape, then wrap each at the base with a wet paper towel then secure all in a plastic bag. Works well.

In your situation it would be best to check before hand to see if Customs will clear grapes coming into your country. Agricultural laws vary widely.

Thanks CharlieBoring.
nandina, what do you mean insert each cutting into a white grape?

Personally, I'd let the ends seal up (dry out a bit) to avoid rot. I'd want the cuttings to retain moisture, but would not want the ends moist.

With woody plants, it's not unusual for people to wrap cuttings in a moist paper towel (or other moist medium) while leaving the very ends exposed.