I think it would be ok if you were to use the foam popcorn. Throw some of that in a box. Lychee in a bag, more foam popcorn on top.
As for the plastic bag, drop a moisture silica bag in it if shipping locally.
If shipping ... like to me in California, Amazon sells gel ice packs. Case of 48 for $13.96
Should help keep it cool for a cpl of days. And package should have arrived or will very soon.
Ok... I’ll be the guinea pig....you can send me a few to see how it works out😉...lol