Joy -- What does "fallow" mean to you?
a) Bare earth?
b) Killed and harvested crop, with residue left on field, but not tilled and replanted?
c) Planted with a cover crop (like grass or clover), between years with a grain crop?
In any case you should be able to find some crop type and management to simulate one of these.
You appear to want to run SWAT for just June-Oct each year, without including Nov-May. SWAT generally works best after it has had a few years of "model warm up" to allow at least hydrologic components (e.g., soil moisture) to equilibrate.
Whether whole areas become fallow or not depends on how you have subdivided your watershed into subbasins, and subbasins into HRUs.
So far from your descriptions, it seems like simply writing the proper rotation, switching an HRU from crop to fallow (and back) over a seasonal sequence for several years will do what you want, yet you insist otherwise. There is clearly something we (at least I) don't understand in what you want to do.
-- Jim