Cheat a bit

Normally, you'd go get a pokedex about now, but you don't really need it for much, and it would reveal your secret pokemon. You head out without it. Sure, you aren't getting a couple free pokeballs, but there aren't many pokemon worth catching around here anyway.

That is, unless you count the southern sea. It's not usually available without surf, but you have something that could work.

You stand on the coastline and take out Smoochum. Pointing at the water, you order, "Freeze it."

The diminutive girl does her best to chill the water, but she can't freeze much at a time. The ice breaks and melts anywhere she's not concentrating, but it's enough to get a few pokemon stuck.

You look over the catch. Most of it's magikarp and tentacool, but you do find something worthwhile. You bring out Charmander to cut the ice around the lone horsea and throw a pokeball. Naturally, the frozen foe cannot resist the capture.