Hello and apologies for the delay in replying, although I don't really have much to add. Having checked my Collectors Coins, I see that they list 4 lines for the 1831 issue:
> no WW
> .W.W incuse on trunc
> W.W incuse on trunc
> WW with no dots ?Exists
but then you already knew that. When I checked my copy of Spink, they only show 3 lines:
> no WW
> .W.W incuse on trunc
> W.W incuse on trunc
with no mention of WW with no dots. Krause lists similar to Spink but their values for the W.W are way off compared with Spink.
I am no expert on these types but if I were to make a guess which variety you have, I would say that it could be either of the two known WW variants but with a combination of a weak strike and a high degree of wear and tear, the dots have disappeared, leaving just shallow remains of the two W's. Just a hunch from an amateur and I could be wrong, would be interested to hear other's thoughts.
Edit: just had a look at Tony Clayton's site
http://coins-of-the-uk.co.uk/penny.html and he only lists the usual 3 lines, no mention of WW with no dots and I also checked Declan Magee's site
http://www.declanmageecoins.co.uk, which is usually quite good for listing all varieties, but either it is just me or there is some kind of server error meaning I can't see anything for William IV pennies. Might be worth sending him your photo to see what he thinks?
Just because you can't see it ... doesn't mean it isn't there - Anon.
Former coin and banknote catalogue referee.