So I started my challenge, took me a while to find a Surskit, I'm happy I was able to catch the first one. I then reached Rustboro without many problems. I also caught a Nincada there. Currently I'm grinding for Roxanne. Main strategy going to be Absorb and Bubble spam with Surskit and Beautifly, while Nincada can support.
Edit: I beat Roxanne, using Bubble for Geodude, then Nincada spamming Sand-Attack and Harden against Nosepass and eventually killing it with Leech Life.
I also beat Brawly using Nincada's Harden and Sand-Attack, after beautifly fell after an unlucky crit.
Now grinding a little for the rival battle just after Slateport.
Another edit: The rival battle was epic. After beautifly Paralysed Wailmer and damaged it a little, Wailmer started to spam Rollout, sweeping through my team, leaving only Ninjask alive. Ninjask then uses Fury Cutter twice, in which Wailmer missed the 5th Rollout! Ninjask then nicely kills the Numel, taking an Ember in the process, then lastly it defeats Grovyle as well!
As I can't use the Pokemart, I assume I cannot use the Game Corner either, but what about Slateport market?