In general, if you have lots of "dust" in one wallet, it may be smart to try to consolidate it into one UTXO - that is, send everything in the wallet to yourself with the lowest possible fee.
If the wallet does not support transactions with artificially low transaction fees and RBF, it may be smart to export the wallet seed (or private keys) into a wallet supporting it, i.e. electrum. Try to send with 72 satoshi/byte in transaction fee - there is a non-zero chance that the transaction will go through during the weekend or the next.
You will not lose the "airdrop"-quality of bitcoins even if you have stuck unconfirmed transactions.
RE: BitMEX dumped their BCH and credited all users!