I would concur with @Adrian_Hills suggestion and use an esp8266 based board (such as the D1 Mini, or a NodeMCU) - these are WiFi enabled and much cheaper than a Pi Zero (even if a Zero doesn’t actually cost that much either!).
Then just flash the WLED project onto it, and communicate with openHAB either via the binding, or through MQTT.
For the WS2812b, just check the number of LEDs that you plan to use and make sure the power supply is rated high enough to power both the board and the strip. I think each LED can consume up to 60mA at full bright white - they’re hungry little beasts! You may want to consider powering the strip directly from the power supply, rather than through the board (which I think is what you’re suggesting already, but just making sure!)