From the entrance plaza of Disney's Hollywood Studios to The Seas With Nemo & Friends pavilion, it's a 1.7 mile walk (I clocked it using a runners' website that has satellite photos). If you walk at a nice clip of 3 mph, that means it'll be a 34 minute walk. And that's IF you walk as fast as 3 mph.
There are taxis waiting outside every park and every resort ... especially the parks. I strongly believe that you can get into a waiting taxi and make it to Epcot's front entrance and walk from there to The Seas With Nemo & Friends in substantially less than 34 minutes. Sounds like 20 minutes tops.
EDITED TO ADD: (And just FYI, it's a half-mile walk from the World Showcase entrance to The Seas, and it's a three-tenths of a mile walk from the main entrance to The Seas)
What time is Fantasmic!, and what time is your reservation. Odds are, you can make it using Disney (i.e. free) transportation. You won't save any time at Epcot, since the taxis drop off in the middle of the bus area - same walking distance.