Are you planning to do this yourself? If you want the best, go with Fil Au Chinois 632 or 832. If you want something cost effective, go with Twist Masterfil Waxed Linen .45mm. Waxing linen thread lightly is always a good idea as it helps with stitching and provides some protection from water. Polyester thread is a different story. Twist Polybraid .45mm in white is not very bright and is thicker than the .45mm Linen. I wouldn't use thick thread on a 20mm alligator strap. Rocky Mountain guys are great. Excellent service and products.
District Leather Supply is very good as well. They carry Vinymo polyester thread which is a good option for you. It is not as tightly braided as the Twist Polybraid but does the job. Their white is bright. Waxing this one is a must IMO. Hope this helps. Any other questions, feel free to PM me!
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