Doves:
As to the position of the stabiliser in the various phases of flight, I encourage you to check your stab trim ind which while during cruise is close to zero,
that statement alone shows in inherent lack of understanding of the B737.
Aside from considerations for it being 'windy', as you put it, on the matter of using a dual-channel approach mode (i.e. both autopilots engaged). There is nothing to stop one from using that mode (see: Boeing FCOM1 / Amplified Procedures / Landing Procedure ILS) even if ones intention might ultimately be to make 'manual landing' (i.e. to disconnect the autopilot(s) at some point during the approach) but wherein (prior to an autopilot disconnect) one then has the facility for an auto-pilot flown go-around (which one does not with a single-channel approach) and / or, putting it in simple terms, just because one engages both autopilots does not mean that one will necessarily be letting the autopilot(s) do the landing, but if one then elects to initiate a go-around (by disconnecting the autopilot and flying it yourself) and doing so when below 400ft Rad Alt, you can expect the said same (dual-)autopilots to have wound in nose-up stabiliser, and which you'd better be ready for when the autopilots relinquish control to the yolk.