Could have had your answer already if you'd checked the 'Restricted Species Lists-by state' in the Marketplace sticky posts. Wels cats are legal in WA state.
I would think if you have a way to prove you obtained it before the law changed you would be grandfathered in, but unless you have proof it would most likely be considered illegal.
Unless there is another list that I'm not finding, It appears to be fine. The restriction I see on there is family Clariidae where as the wells is family Siluridae. If you have concern your best bet is to contact them and ask.