I would pinch it between 2 rollers, with a bit of pressure exerted (like spring tension).

Similar to what you'd find in a pasta machine. If it works for noodles, it'll work for string.

The clamping force creates the friction you need to get an accurate reading, the resistance of turning the rollers will create tension you need for a clean wind onto your small spool/card, and you can calculate the length based on roller diameter/revolutions (either with a gear, an optical encoder, or just counting revolutions, depending on how far you want to go).