other than correct technique and proper footwork, what exercise do you recommend to increase stroke power?
yap. those core muscles come in handy when you are late at back court. some finger/wrist won't hurt either.
double skipping rope - self explanatory, good for wrist/underarm, in malaysia and china they often finish with about 1000 double skips after practice sessions as it helps with so many things. flipping wrist with racket in hand - a bit like doing underarm clears, heavy racket preferred. push-ups as already mentioned - there are lots of variations of this to make it more difficult or using more muscles, like clapping between each, wide arms, arms in a lower position, one armed and so on... face a wall and hit hard with shuttle - at a high tempo it's a lot about learning when to relax and when to tighten grip in order to generate the most power with least amount of strain - also common to grind in asia. and maybe masturbation...
curios - biceps mentioned first here, but biceps play minor role in badminton - they only come into play during supination... I also disagree with the 'many repetitions' bit - you shouldn't be training your muscles for endurance but for explosiveness. This would need medium-heavy weights where you can perform the contraction fairly fast, but for a low or middle-ing amount of repetitions. If you can do many repetitions then the weight is too small to helping your explosive muscle development
Biceps minor role? You are mistaken my friend. Muscles work in pairs and for best performance should be trained together. For weights, I recommend 25 reps and keep on increasing the weight in small increments as it becomes easier. Movements should not be too fast else mementum will take over instead of muscle contractions across the full range of movement.
muscle pair balance is of course important to avoid injury. but bulking up biceps won't help the vast majority of your badminton shots.
This is not about bulking. If you could numb your biceps, you would know how important it is to the overall stroke movements & strength. Spot training muscles will never work effectively in sports like badminton. One should work all the major muscle pairs i.e forearm extensor/flexor, biceps/triceps, chest/lats, stomach/back, quad/hamstrings etc etc.
From my experience no. My smashes and shots became more powerful after I started doing curls and extension with free weights. If you can do only few exercises, I would just do squats, pullups and pushups. Can you manage high rep pullups? If not supplement with some curls
you can strengthen your core muscles, but if you don't know how to use them effectively to transfer power into your shot (ie. via the kinetic chain from proximal to distal into the fingers), then it's of no use