The products I mention below are all Bainbridge products. Images were taken from the Bainbridge Sailmaking Hardware Catalog, which you can download at
http://bainbridgeintusa.com/wp-content/uploads/2016/04/bi_sailmaking_hardware_catalog.pdf
If your measurements of 3/4 inch wide and 1 1/4 long are accurate, it's probably an A008 slide from Bainbridge. (or an A006M - pictures would help) Available on SBO at
https://shop.sailboatowners.com/prod.php?664
Compatible plastic shackles are either a Bainbridge A023, A027, or A035BK . Choose the one whose length matches the existing shackles.
SBO sells the A027 but not the other two at
https://shop.sailboatowners.com/prod.php?660
If the shackle is metal, it might be a B303 or one of the following:
SBO sells some metal sailmaker's shackles at
https://shop.sailboatowners.com/prod.php?14506 , but I'm not familiar with the part numbers. One may match your others.
Choose a shackle that is the same length as what you have, so the slides stay properly aligned vertically.
Challenge may have similar items with different part numbers, but most sailmakers use the Bainbridge part numbers.
Niether Challenge nor Bainbridge sell small quantities to the public, but you can google the part number to find an online reseller.
The choice of attaching with webbing vs shackles varies with the application, according to the alignment and articulation requirements.
PS. The catalog lists nominal measurements. The actual measurement using a caliper are usually smaller. An A008 is a little narrower than the nominal 19mm. Using my caliper, it says 17.89 mm.
PPS. It could be an A006M which has a nominal width of 20 mm, but measures closer to 19mm. It is compatible with A023 and A027 plastic shackles.