For another way to send BTX from Trezor, without using Electrum but still without exposing your private keys, I posted instructions on reddit a few weeks ago:
https://www.reddit.com/r/BitcoinAirdrops/comments/7drt94/claim_bitcore_btx_without_compromising_trezor_seed/dq9tir4/(But it requires more manual work and a Python script; Electrum is a lot easier.)
One issue with holding BTX on Trezor is that you can't sign a message to register for airdrops (because BTX wallet software uses a different prefix string for message signing than BTC wallets do); the Trezor firmware would need to be changed to add support for BTX message signing. (This probably wouldn't be hard for someone to add though.)
Also, if someone used their seed words to get their private keys, but has BTX on segwit addresses that they don't know how to import into the Bitcore wallet, here's a way that worked for me:
At
https://iancoleman.io/bip39/ use the BIP32 tab, and for BIP32 Derivation Path use m/49'/0'/0'/0 and copy a private key and address (which starts with a 1; this isn't a segwit address yet).
In the Bitcore console (Help->Debug window, Console), type "importprivkey YOUR_PRIVATE_KEY test false", then "addwitnessaddress YOUR_1_ADDRESS". That should give you a segwit address starting with 3. Repeat this for other addresses. Then close the Bitcore wallet and restart it with -rescan which (after a few minutes) should make it see previous transactions to your addresses, and you can then send from them.