Practices which are Tibetan Buddhist and Mahayana but not Vajrayana:
Lo-do Nam-zhi (The four topics that turn the mind)
You might want to do word searches for those topics. These are very wonderful, very powerful and positive practices.
Also, the three lower tantras (kriya, carya, and yoga) are tantrayana, not, strictly speaking, Vajrayana. Vajrayana only refers to the three higher tantras (Maha, Anu, and Ati). Some of the practices others have suggested to you, such as Tara and Medicine Buddha, are often practiced from either the sutra or tantrayana POV or level. When practiced from the sutrayana level, no absolute need for a Teacher. Best if we all reserve the word "Vajrayana" to specifically mean (at least within the Nyingma school) the three higher tantras.
Thank you! Thank you thank you thank you!!
THAT is exactly what I wanted to know. Now I can try to find out some of the specific practices, observations, meditations, etc. of these traditions, if there are any specific to these practices.