Well, I give them a preconfigured executable: the window looks similar to Explorer, and there's the remote server's content, and it asks for password at startup

Well, I give them a preconfigured executable: the window looks similar to Explorer, and there's the remote server's content, and it asks for password at startup - but it's actually WinSCP with pubkey auth. Compressed, resumable, recursive, and reasonably secure (audit ahoy!). Mac has SFTP support built in, as does Linux - no issues there.