I’ve purchased several guitar tuners over the years, but the D’Addario NS Micro Headstock Tuner is the smallest clip on tuner that I’ve tried so far. It’s only 1.25 inches long and can clip on a wide variety of stringed instruments such as guitar, bass, ukulele, banjo, mandolin, and more. Its adjustable ratchet clip and rotating reversible screen allows for placement on front or back of headstock. It’s small enough to leave clipped on the headstock and features accurate chromatic tuning based on vibration, no sound or cable input required. It runs on one CR2032 coin cell battery and has an auto shut off feature after 10 minutes of inactivity. The NS Micro Headstock Tuner is available through various online retailers including Amazon, who offers it for $11.49 for one and $23.34 for a 2-pack (Prime).
I’ve been using one of these tuners for a few weeks with my ukuleles and really like the small size and the fact that I can leave it on without it rattling as I play.