The ruling on performing the full ritual bath for major ritual impurity when using a capote

The honorable Shaykh! If a man wants to have intercourse with his wife, and before he has intercourse he puts on something called a "capote" which is sold in pharmacies, and when he had intercourse he did not ejaculate, is the full ritual bath obligatory for him or not?
The full ritual bath is obligatory for him as a precaution.Otherwise, some scholars say: In this case, the full ritual bath is not obligatory for him; because the private parts did not meet.