----- I am not an ESL teacher -----
I think you can use both, although "on one hand" is somewhat more usual.
Yes, "on the one hand" looks more formal, but it could be just an impression.
A slight different could be the following:
If you first state that you are going to present two confronting situations, than you may use "on the
It has pros and cons: On the one hand ... On the other hand ...
However, if you begin stating the first confronting situation, then you are more likely to use "on one hand."
Well, on one hand ... On the other hand ...
Finally it is important to note that you can also use only "on the other hand", without its accompanying pair, if you recall the expression only after you have already introduced in the first confronting situation. Take a look for instance at: https://www.usingenglish.com/forum/ask-teacher/104219-other-hand.html
It would be interesting to read a native speaker about this point.