Fight Safari Pokémon Elsewhere
To fight and capture Safari Zone Pokémon outside of the park, first go into the Safari Zone. Let the time run out when you're standing in a patch of grass which holds the Pokémon you want to catch. Step back outside and use FLY to Fly back to Cinnabar Island. Using SURF, surf up and down the right side of the shoreline, where you are half on shore and half in the water. You should then enter some battles with Safari Zone Pokémon! Now you can attack and capture them with Ultra Balls. This also works with other areas of the game where you find wild Pokémon.