Yes. Formalise it. If anyone arouses suspicion then don't proceed.
It used to be an easy answer once all the legalities were addressed, but, the current virus puts a BIG question mark after the question. If you want to know the legal questions, contact me.
It is always a more productive work environment when you can be in the presence of your co-workers and work partners than when you have to overcome a gap. You will never be able to look over someone's shoulder, overhear, or inspire with your presence when your partner is thousands of miles away. It doesn't mean you can't succeed, but it will always be more difficult than someone who can sit next to you, communicate with non-verbal signals, and be observed.