First let me say that I am not a licensed electrician. I do have a good bit of formal training and hands on experience with electricity and electronics. That being said, I doubt that an electrician would tell you any of this is acceptable according to code and the following information is strictly my opinion, so proceed at your own risk.
Providing that both timers receive their power from the same circuit, I don't see why not. As for the diodes, I figure you obviously understand their purpose would be to prevent back feed to the inactive timer or you wouldn't have known to ask about using them. But, since the contact of the inactive timer should be open while it is inactive, I would not expect you to need them. But that is going to depend on the circuit design of your timers and the way you wire it all up. But rather than worry about the timers overlapping or back feed, you could do this with a single timer and a relay/contactor, providing that the relay had both NC and NO contacts and it is capable of carrying the amp load of the two fans. That way you'd never have to worry about multiple timers and overlap.
A licensed electrician would probably have heart murmurs if he saw my setup. I've got a 24 hr timer, a minute timer, a delay relay, a standard relay and a fan speed control wired up so that if my power goes out/blinks, my fans (circulation and exhaust) come on as soon as power is restored while my HPS is delayed 5 minutes to allow cool down to eliminate hot restrike. When my timer turns the lights out, my minute timer will kick in and run my fan approx 3 mins on for every 15 minutes to keep odor in check and help keep temps down and air circulated. Odors haven't been an issue for now so As summer is getting here, I'm about to change the minute timer out for a thermostat control to only run my fan when temps get too high because I don't have AC for my grow room. LoL
. Hahaha. Anyway he said a "two channel timer", but he wanted almost $300 which is f@#king ridiculous. I am yet to research these and see if they would actually do the job.