Creating a message authentication scheme
Doing this would not be secure.


If you truncate the SHA-1 to 64 bits before encryption, then anyone can find a collision in about $2^{32}$ tries (taking minutes on a desktop CPU), and by finding the encryption of one message hash also learn the other. Even a second preimage attack may be feasible.
If you use ECB mode to encrypt a longer hash, then the attacker can attack it "piece by piece", finding one hash value that collides with several block-aligned parts of earlier hashes. This is more difficult than finding a 64-bit collision, but much easier than finding a full collision.


The best you could hope for would be somewhere between 60- and 70-bit security (collision search on full SHA-1), but that would require better encryption/MAC on the hash, and would be more complex than simply implementing HMAC or CBC-MAC.



If the dongle can do (semi-)arbitrary things with 3DES and the PC can do arbitrary things, then I would recommend:


Using a longer hash, e.g. SHA-256, on the PC: $h = H(m)$
Using a block cipher-based MAC on the device on the hash: $t = M(k, h)$.


That gives you the weaker of:


the collision resistance of the hash (128 bits for SHA-256) and
the security of the MAC.


The block cipher based MAC could be e.g. CBC-MAC. That is simple enough and with SHA-256 you would only need to process four blocks on the device itself.