I can fill in some details from the Court of Orphans records and the probate record:
8 April 1651: Anne Smith (widow of William Smith, woodmonger), now married to John Haslegrave of Limehouse, are bound to provide an inventory of WS's estate.
15 Jul 1651: Felix Wombwell, mariner of St Giles Cripplegate, is additionally bound to provide an inventory of WS's estate.
31 Jul 1651: all the above (Anne, John and Felix) -- having supplied the inventory -- are bound to secure the portion for the orphans
30 Mar 1652: the estate is secured (£737 and £562 legacy money) for two orphan daughters Joan and Fortune. (Note that Joan is likely the older of the two)
8 Mar 1652/3: Fortune is licensed to marry John Dorrington, mariner, subject to his providing her with a jointure.
23 Nov 1654: Fortune and John declare satisfaction of her portion.
The early inventory bonds indicate that WS left an administration rather than a will. There is a PCC administration for a William Smith of Stepney for 1649 which says "renounced and will pr. Oct 1650". So I checked the online PCC index, and there is a will for WS dated 23 Oct 1650. So you're in luck!
It's not clear what happened with probate, but possibly the Anne took out an administration and subsequently discovered that a will had been made.
The Woodmongers' Company was dissolved relatively early and unfortunately no company archive survives.
cheers,
Mike