Tandy Leather retail stores
(and online) sell the repair awl kits, and the various coarse threads they carry are just what you need.
But, back in the Dark Ages, I became very nimble fingered with a simple Velox tubular repair kit which included the thread, an upholstery needle and a thimble. The Clement Seta track racing "silks" were only 6 ounces (thats around 170 grams INCLUDING the tube) and had virtually a painted-on rubber strip over real silk casing. They were so expensive and delicate you would ONLY use them on a wood track. The comparatively heavy 12-13 ounce "training" tires were still expensive (to me!) and so I would just spend quality time on occasional Sunday evenings playing the dutiful little seamstress laboring over a half dozen punctured tires. You'd be surprised how fast and efficient you can get at repairing tubulars... when you can't afford to toss out tires.
It was still always a nuisance. But, we all considered it simply part of "paying our dues" as a serious cyclist.