It definitely wasn't Walter. Maerlyn says one of the Red King's emissaries caught him. We don't know who the emissary was - could be just an original character or, if you like finding connections, it could have been Leland Gaunt as this particular emissary was described as playing the part of a wandering peddler, a description used for Gaunt in Needful Things and also Gaunt's form in Mid-World, if the Peddlers Moon poem is to be believed:

Late summer moon
Huge and orange
And the Peddler, who comes out of the Nones
With his sack of squealing souls
(Leland Gaunt carries a sack of squealing souls in Needful Things.)

However, it's stated that once he was caught it was the Crimson King himself who changed Maerlyn into a tiger, albeit from afar.