In a medium bowl (or in a blender), combine the almond butter, coconut milk, lime juice, and curry paste. Whisk or blend until well-combined and smooth. Reserve 1 cup of the mixture and refrigerate (to use for serving later). Place the chicken pieces in a container with a lid or in a gallon-size ziploc bag. Pour the marinade over the chicken, tossing so the chicken is evenly covered. Refrigerate for 15 minutes (or up to 12 hours).
For the cucumber salad, in a medium bowl, add the cucumber and bell pepper. Whisk together the lime juice, rice vinegar, olive oil, and pinch of salt and pepper; add to the vegetables and toss to combine. Refrigerate until ready to serve.
Preheat a grill (indoor grill pan or skillet will work, too) to medium or medium-high.
Remove the chicken from the marinade (the marinade will be very thick, especially if it has been refrigerated longer than 15 minutes; that's ok - just take the chicken pieces out and scrape off any excess marinade). Thread the chicken onto skewers. Grill/cook, turning once or twice, until chicken pieces are cooked through, 7-9 minutes.
Serve the chicken skewers with the cucumber salad and the reserved almond coconut milk sauce (to drizzle over the chicken, if desired).
