The way I see things now, going forward there are at least two systems we can employ on the basis that we sign Walcott but fail to bring in a LB. With Coleman coming back soon I honestly don't think we'd be looking too bad until the summer:
Against 'non-top six' teams at home:
Pickford
Coleman - Holgate - Jagielka - Kenny
Rooney - Gueye
Walcott - Sigurdsson - Bolasie/Lookman
Tosun
Think this one is pretty straightforward. Rooney is at his best when he's finding space with the ball to bring out of the midfield. Plenty of options in front of him to work with. Bolasie & Lookman are much of a muchness out on the left though I think Bolasie gets the nod by virtue of his distribution being better (I also happen to think Lookman, by and large, would be more effective coming on as a sub). Jags gets the nod over Williams due to him generally making better use of the ball from the back, though that's not really saying an awful lot.
Every other scenario:
Pickford
Holgate - Keane/Jagielka - Williams
Gueye
Coleman-----------------------Kenny
Davies
Walcott----------Sigurdsson
Tosun
I appreciate this one looks a bit bonkers but I think it could work. It's essentially a back five with Coleman & Kenny as wingbacks, which both are capable of doing. In both Walcott and Sig in front of them they have players who are good on the ball and will provide an outlet. Rooney is dropped to the bench with Davies getting the nod, as a CM I think his off-the-ball productivity is a bit better than Rooney's whilst still possessing the quality to be able to attack with the ball when he gets the opportunity to (certainly when his tail is up). The likes of Rooney, Bolasie, Lookman, Vlasic and even McCarthy would be good options off the bench depending on the situation in the second half of matches.
Just as a side note, and I say this quietly, but I think Klaassen could potentially also work in Davies's position in that system.