Washing, finishing with a cold splash should clear any residue from previous sprays. But in my view the anti-perspirants interfere with the body's natural breathing. In this 'modern day and age' with male and female staff sharing offices etc., it seems ordinary sweating is out. After a while you sweat with nerves, worried about being 'fingered' for body odours. You apply more anti-perspirant and it builds up, leading to itchiness. It's a product of the environment in shared premises, and men are not the only 'sufferers'.
I don't have to worry now I'm a 'state employee' (pensioner), but I do have to keep up standards where I work part-time for the MCC at Lord's - in and outside the Lord's Museum at County fixtures and Test Matches at their ground in St. John's Wood, London NW8. It's nowhere near as bad as in an office, though.