Is there a form of tai chi or yoga that can be self-taught?

The simpler styles of Yoga, as some can be dangerous without the aid of an instructor, can be self taught, as well as the Yang, Hao, Wu, and Sun styles of Tai Chi Chuan if all you want to do with them is exercise. However the Chen style of Tai Chi is very, very dangerous, as it uses a lot of leaps and squats requiring guided specialized conditioning under expert eyes. If you do not have a teacher closely observing your stances in the Chen style, you can very easily blow out your knees. Its the same thing with Shaolin Kung Fu; its more advanced routines can be very dangerous if you do not build up to them under the watchful eye of a teacher.

However, the other 4 schools of Tai Chi, are benign enough to be self taught. If you wish to learn them as Martial Arts you need to;

1) Condition yourself to eventually hold mabu (google it) for 4 hours.

2) Practice the given Tai Chi routine for at least 3 hours a day every single day.

3) Push hands with a more advanced student, or your teacher, once a week, to gain a feel for how momentum applies to the human body.

If you do not meet all 3 of those requirements, no Tai Chi style can used as a martial art. Additionally like all Kung Fu, Tai Chi Chuan uses chin na, advanced joint locking techniques reliant on momentum. If you do not know how to properly time when to lock a punch or kick, a chin na lock won't work. Chin na, operates on the principle of using an opponent's attack against them in order to trap them. Simply put, an attacker's attack helps you, the person defending, trap himself. The harder he strikes, the tighter and more painful the lock. Because a lot of men can strike with extreme power and speed however, the timing needs to be precise, consequently the need for repetitive drilling, and patience spanning years, decades even.