OK, don't know if the combo'd work:
M93 C/W glaser (round1) shotshell (round2) birdshot (round3)
DITTO ABOVE For offhand, both with 15rnd mags.
A couple of .44 wheel guns in shoulder holsters with Glasers
I don't think a full auto would be of much use, so, a 12 guage dual barrel (cut right down to next to nothing with 00 shot, maybe some solids)
& also over the back, a couple of long blades (lightness counts for close work as well as length) & as those zombies are a tad slow, those there Tramontina machetes, sharpened up'll do the job better than a 24" blade katana up close & personal IMHO