Yes but try a traditional Greenland kayak paddle
You absolutely can although as mentioned above you are sitting closer to the water and may therefore need a shorter paddle.
That said, as your seated posture is different (if you really want to take advantage of the narrow kayak hull it’s best to be low and “locked in “ to the hull with your thighs) you may find the paddling ergonomics vary enough that you may not see the benefit of all your muscle memory.
You can also sit in a canoe-seat posture in a kayak, which gives you your strong familiar paddle ergonomics but raises your center of gravity and wind profile substantially. if the kayak is wide and stable this may serve you well, you will have a canoe-like craft which has lower freeboard so it will catch less wind, and better protection from chop (especially if you use a spray skirt).
However, a kayak paddle gives you the ability for instantaneous, instinctive brace strokes (strokes to keep you upright if tipping) on either side of the boat without having to move the blade over your body. That’s part of what allows you to paddle a more narrow, more tippy hull in rough water with great confidence. In turn, the narrow hull pierces the wind and chop, and the low-seated paddler hides from the wind. This is great for the ocean of course but it’s also great for a long day exploring a lake where breezes can kick up short steep waves before you get back home.
You may also really enjoy learning a new paddle (just as you apparently have embraced learning skills with the canoe paddle).
I would recommend at least trying Greenland paddles (pictured—-full length and “storm” length which is paddled much like a canoe paddle), they are equipment designed by subsistence hunters and can be paddled very quietly.
Also, if you’re shopping for a kayak: Borrow a few or find a shop that lets you demo gear before a final purchase and spend enough time in higher performance hulls to get past the initial feeeling of instability, before deciding on the amount of tippiness that fits your needs. I for example love fast boats but in practice want to be able to take a photo or eat a sandwich so I stay with touring hulls vs either racers or recreational boats.