Marinate the chicken strips in the lime juice and sesame oil for 30 minutes, then pat dry with kitchen paper and season with salt. Place the sesame seeds on a plate and roll the chicken strips in them until they are coated.
Heat half the oil in a wok over a high heat until the oil starts to shimmer. Toss in the chicken strips and stir-fry for 2–3 minutes until golden, then tip on to a plate.
Return the wok to the heat and wipe it clean with kitchen paper. Add the remaining oil and, once it's hot, tip in the peppers and pak choi and stir-fry for 2 minutes. Stir in the soy and sweet chilli sauces and cook for 1 more minute, then return the chicken to the wok and stir-fry for 1–2 minutes until cooked through.