No, not silly, especially if they have a longish coat. My GG's have quite flakey, dandruffy stuff in their coat, and a bath with "Head & Shoulders" (the one with conditioner in it), really clears it up.
However if you suspect lice - either Eprinex (for cattle - and quite expensive, also kills mange/heel mites) or Coopers Spot-on (for sheep, also quite expensive) will do the job.
If he skin is scabby then a Dectomax injection would kill the mites that are the same as scab in sheep, can't quite remember the name of that type of mite... Your vet should be able to give you a single shot of Dectomax already in the syringe. One shot should do it.