You originally asked if it’s against halacha.
Why don’t you ask your rabbi?
(I’m sure the psak would be entirely different for different people, depending on their expertise in Tanach etc.)
Regarding debates, in my opinion it’s best to steer clear of them altogether. It’s easy for anyone to skew a debate in the direction they want it and often it’s the more charismatic person who “wins” – not the one with more knowledge.
There are a lot of other important ways to do anti-missionary work.