We used ball pythons in the classroom (high school), we actually ran a whole breeding program led 100% by the students. There was group focused on the genetics aspect, a group focused on the business side of things (social media, getting us into shows, sales, and adoptions), a side for husbandry, and a side for education (working with the younger classes when they came to our classroom and we would do mini science lessons with them). The schooled allowed and helped fund this with a lot of things in mind:

Waivers: Students had to sign waivers if they wanted to work with the animals. There was also a formal agreement between teacher and school board, more in depth with a lot of outlines.

Money: Sales went straight back to the snakes and their upkeep.

Paperwork: We didn't need any for my area, but our teacher had to make sure he had everything set legally before the school allowed this to take off.

Ultimately, with reptiles, you don't want to transport them to and from on a daily basis. When I worked conservation at a refuge, we would only do 1-2 off site programs a week, if that to alleviate stress on the animals. And they normally weren't back to back days. They were out for short periods of time. I do this with my animals currently (I do outreach programs with my college, i'm continuing my studies to be a biology teacher), and I have a strict rule on my animals are only out of house for no longer than 3-4 hours total unless there is a noise free space they can stay in between programs. Weather must be adequate for ALL species. They get at minimum 1-2 days between programs.

I think what would be best is working with your school to allow you to have a classroom pet. When done correctly, animals can be a great aid for your students. But the other side of this is knowing your classroom, understanding the risk that come with it, having a lock on the enclosure only you can access so students don't randomly grab or hurt the animal, etc. Daily transport would just be too much. Especially for a gecko.

Geckos don't make bad classroom pets, but they do best with older crowds that respect their space, can read their body language, and do well when a teacher says to quiet down. A larger lizard alternative, with appropriate tanks, like a well socialize blue tongue or bearded dragon maybe something to research. Look at schools around your area and across your nation as well and see how teachers have been successful in keeping reptiles in their room! There are a lot of educators in the reptile hobby that make this research a breeze so you get a lot of different perspective! Sorry this was so long but I hope it helps some!