Trading with gun dealers
When I want to estimate the value of a used gun I go to Gunbroker.com and find some auctions for the same gun in the same condition, looking only at "no reserve" auctions. Here is an auction for a 4 inch barrel S&W 686 in "excellent" condition, prelock, for $475:
S&W 686 for $475
And here is an auction for a brand new S&W 637 for $360 on Gunbroker:
S&W model 637 for $360
So I would say, based on this, that the 686 is worth about $115 more than your "like new" 637, if you were trading with the previous owner of the 686. But a dealer wants to make a profit margin on the deal, and he can buy a new 637 from S&W for wholesale price, something under $360. So I am not surprised that he would ask for $200 in addition to your 637.
Your only real alternative is to sell your 637 directly to a buyer who is not a dealer and try to get about $320 for it, then pay cash for the 686. But you have to find a buyer, which may take awhile.