I know people who have gone on caving expeditions to remote areas with very minimal baggage allowance and have therefore got on the plane wearing as much cold weather safety and camping equipment as they could get away with. I'm not sure how many of the stories are apocryphal (or just old enough that security personnel were a bit more flexible on the crucial points), but I'm reliably informed that wellies rolled up and stuffed into the pockets of the coat you wear onto the plane do not count as part of your weight allowance. On the other hand, putting a large spanner inside one of your wellingtons which is inside the other wellington (upside down) and then stuffed into the rucksack you're taking on as hand luggage is not recommended, even when it turns out that the non-English-speaking security staff are merely bemused rather than suspicious, because explaining the maintenance of caving gear and what you've been doing with it via the medium of mime is surprisingly tricky.

Anyway, how you go about acquiring a coat with sufficiently large pockets and then not expiring from heat exhaustion in hot airports afterwards was not specified, so this is probably not helpful advice.

I hope all the travelling goes well!