Soft snap blocks

[benz]

As you suggested yourself, chafe would be an issue. A teardrop thimble would run the (small) risk of turning upside down, leaving the line around it to chafe on the sheet, or squeezing itself back shut as the line cinched around it. In the past I've clipped a suitably-sized carabiner to the sheet, and hauled it down with a tackle. For the most reliable and lightweight, if you don't want to spring for a Colligo setup, reeve the sheet through a bullseye fairlead (Antal calls them 'Low Friction Rings'). It will sit innocently against the genoa track car until needed, at which time you can slide it forward into position, attach a tackle to it with a soft shackle, and haul away. Done that way, you always know where it is, and it can't go overboard.
Ben