Really 1/4" Fiberglass 55-SLVF04BLK (TMB part number) would work best over that of a larger 3/8" sleeving size.
Overall, the
ETC stain relief clamp is designed for a type #0 / 5/16" size of sleeving with what 16ga. wires are within it. A different sleeving could either stress the conductors or be too loose on the tension given a smaller size.
I have found that type 3M #69 fiberglass Electrical tape placed right under where the
strain relief is helps a bunch in wear problems at the
strain relief. Other than that, for an
ETC Leko... don't mess with what is the proper part. 3/8" would be messing with that and a huge
jacket over the conductors. This
fixture is designed in
cord grip for a #0 or 5/16" sleeving and that's the proper size to use.
On the other
hand... speaking of McMaster Carr... they also sell a #0 size of vinyl coate sleeving. Such sleeving is a
bit more abrasion resistant than normal fiberglass sleeving and in general is better to use. Otherwise McMaster #7468a22 Pliobond Universal Cement #20 for Nonporus Surfaces, seems to work really well in gluing back together frayed holes in jackets to cords as long as not too big. At some
point, wet the frayed strands and glue them back together if not too large a hole. Saves tons of money.
Vinyl coated sleeving lasts longer, but otherwise where possible the rip or hole isn't too big, repair it. After that, I would only use a proper sleeving for the
fixture to replace it.