First I have to ask. Did I miss some errata someplace? TacOps states the DA for a medium shield is 5, and its DC is 18, but the RS for the 5H shows 4 and 17.
Barring that..if its 5, then the medium shield is going to be surprisingly effective against the Shiro's LRMs. It will absorb all of the damage from impacts against the protected hit locations, and while each one will reduce the DC, you're still having to chew through the shield without doing any damage. The good news is that each LRM10 can possibly do 2 hits, so you don't have to chew through half your ammo to get rid of the shield.
You can try to dance at range with the LB2-X as well. You've got the ammo the speed to do so, but since its an IS LB-2X (Why they didn't go with a Clantech LB-2X, I don't know. What, would it have been too munchy?), you only have 2 hexes before the Black Knight starts replying with its Clantech ERLLs. Those Clantech ERLLs that are tied to a targeting computer (true, one of them will take a penalty for being on an arm with a shield, but that can be partially negated).
I think it will be an interesting fight, but I think the Shiro is 400 BV under the Black Knight for a reason.