Actually, for you, you don't really need a loading chute, since you have a small number of cattle. So you might be better off with using a goose-neck trailer for hauling instead. BUT, if you so insist on having a loading chute, then so be it.
Cattle move better directly from the crowding pen to the loading chute, rather than moving through a long working chute. Desirable characteristics for a loading chute include curved approach, solid sides, telescoping side panels, self-aligning dock platform or bumper, and circular crowding area.Th e slope of a permanently installed cattle ramp should not exceed 20 degrees. The slope of a portable or adjustable chute should not exceed 25 degrees.
For loading chute:
Width: 26"
Minimum length: 12'
Maximum rise: 3.5'
Radius of a curved chute: 12 - 17'
Spacing of 1 x 2-in. hardwood cleats: 8
High tensile wire fence, in my opinion, should not be used for loading/handling animals. You need a solid board/steel fence (holding area/crowding alley) to work them in, and since your going to build a portable loading chute, your better off with building a whole separate pen (FOUR sided, not three) that's not connected to your HTW fence in anyway. So a holding pen of about 12' x 12' should be sufficient, then have a holding alley that's about 10' wide connected to the holding pen. The end of the alley, on which ever way you plan, would start sloping inwards toward the opening of the loading chute, with a gate at the end of the beginning of the tapering alley.
My two cents.