Yes you can wear both.
Strong deodorant for me does seem to have a negative effect, lots of people on hear use natural unscented deodorant, I use a spray made from salt crystal that works great for me.
As far as using other cologne’s many users do use a cover scent, but be aware different colognes can affect diffusion of mones aswell as silage of scent so this may also change your results.
You may find this thread interessting Good aftershaves + deodorants that ladies love!