Glad to see Ithica opened it's doors a couple of years or so ago.
Home of The Ithaca Gun Company
I'm not sure about the recommendation to dissassemble the stock for cleaning, but I'm not posting to dispute.
That said, a pump can be easily cleaned partialy due to the fact that they don't get extremely fowled in the action. Sure, if you drop it in the mud, it might need a good detail cleaning.
On the 37, open the aqction and stick a tooth brush up it's action, follow by a wipe of the rag or even a little compressed air if available. Clena the barrel as normal. Shouldn't be a big deal.