First off, we have factual information about Zoras evolving, or a better word,
adapting, to become the Rito tribe:
Aonuma: "We created the Rito as the evolved form of the Zora that appeared in "Ocarina of Time" and the Korogs as what the Kokiri became once they left the forest. They appear different, but they have inherited their blood."
Why the change though? It's obvious that the flood played a vital role in all of this and it's basically survival of the fittest in a way. Zoras had to adapt to fit the new surroundings. Zoras are quite domesticated and reside typically within rivers - the only anomaly was the Great Bay in
Majora's Mask. However, that was still shallow water one could potentially argue. Anyway, I think the Great Bay also gives us an insight into how Zoras would suffer if they were in fact exposed to large warm ocean waters. Remember how the tribe was in turmoil when we first set out sights on the bay? This could have been their fate in
TWW had they not adapted. I hate to bring in real life scenarios, but river creatures--in most cases--wouldn't survive in the ocean. The salinity, the depth, the food, the weather, the temperature, the threat from predators and competition for food. You also have the fact that the Zora's need a safe place to store their eggs to ensure the race thrives - this would be under severe threat in an ocean habitat.
I'd like to think those, what I listed above, are all valid reasons for the adaptation the tribe had to make in order to survive. Why birds though? Well Hyrule has basically become one big ocean with vast isolated and segregated Islands. Communication would diminish greatly, which is why Hyrule needed a race to fit the role of a messenger: the Rito tribe. There was a reason for this transformation and I really doubt that 99% of the tribe made the transition to human-bird hybrids while the odd Zora turned into a fish. Evolution doesn't really work that way.
If we were going to go with this though, I would have a number of problems. The first being the appearance. Merman [Fishman] doesn't appear anything like a Zora - there is literally no sign of any connection between them rather than them being water based animals. Zoras have one definitive trait in my opinion - they're hybrids. This is what makes them so unique. They can walk on land and do humangly things, while they also have the traits of a sea creature. The Rito tribe is somewhat similar, they are very human like, but they share many similarities to bird-like animals. (I'm mainly taking about the civilised Zora race and not the enemies seen in the older games; however they too shared this hybrid-like trait.)
The only connection I can really see is the fact that Fishman can swim; however that's not enough evidence to really convince me.