The chance of encountering a shiny in the Safari Zone is the same as everywhere else in the game - 1 in 4096. When encountering Pokemon in the wild, this chance can be increased in two ways:
- The Shiny Charm (Key Item) triples the rate you can encounter shiny Pokemon (3/4096, or roughly 1/1365)
- Chaining (encountering the same Pokemon over and over) can boost the rate up to 40 times more (after 40 of the same encounters)
Pikachu appears in the South East region of the Safari Zone - if you try and encounter it elsewhere it won't appear.
You may also want to consider putting a Pokemon with Static at the front of the Party, rather than Cute Charm - Static will increase the chance of running into an Electric Pokemon, whereas Cute Charm only increases the chance of running into the opposite gender. Electrike, Voltorb, or (funnily enough) Pikachu all have the chance to have the Static ability normally.