I think it should work if you generated an unsigned transaction from a watch-only wallet's latest version it will generate a PSBT file you can then import it to your electrum 3.8.8 and be able to sign it. And transfer it back to a new Electrum wallet to broadcast. -snip-
Unfortunately, the PSBT export from the latest version down to 4.0.1 aren't compatible with the lower versions 3.3.8 and below.
He either have to downgrade the watching-only wallet into v3.3.8 or upgrade the cold-storage to v4.0.1.
Release Notes:
# Release 4.0.1 - (July 3, 2020)
-snip-
* Partially Signed Bitcoin Transactions (PSBT, BIP-174) are supported
(#5721). The previous Electrum partial transaction format is no
longer supported, i.e. this is an incompatible change. Users should
make sure that all instances of Electrum they use to co-sign or
offline sign, are updated together.