Common sense is best defense here. Many anti-malware programs are trojan's themselfs. Even if anti-malware program is legit, its never guaranteed it will be able to protect you!
You doing it good, maybe a little bit overkill with not even actually reading emails but if you are using email software like outlook or others it can protect you against 0-day explits on email software.
In the end there is no limit to how secure you can be, you can always spend some extra time to do something more secure way. Laziness is biggest enemy then