New England Dyneema Chafe Sleeve

[Rigtek]

Looking to add some New England DCS Dyneema chafe sleeve cover to the ends of a few new stripped halyards. The sleeves will only be installed at the shackle end of the halyards for only 4-feet. I'm assuming the core to core double braid eye splice with these is the trick but does anyone have any experience with which diameter (cover only) size to purchase?

Lets say we are adding the cover to a stripped 5/16" 12-strand double braid (outside dia = 5/16" / core = 3/16")

and

Lets say we are adding the cover to a stripped 3/8" 12-strand double braid (outside dia = 3/8" / core = 1/4")

Anyone have some experience here in regards to the proper diameter cover to use to allow enough room for the crossover for both a 5/16" and 3/8" 12-strand doublebraid?