It should be sufficient to use the hardware serial port to receive MIDI and send MIDI. Your sketch would receive the MIDI messages, recognize which byte is the velocity byte, and output the same message with the velocity adjusted.
If you want to get fancy you can use a potentiometer on an analog input pin to adjust the velocity limit on-the-fly.
I think the Arduino Pro Micro would be the best solution. It has built-in USB (for upload and debug) PLUS a spare hardware serial port (for MIDI). The Arduino Pro Mini is small but only has connectors for one hardware serial port. You need a separate USB-to-Serial board or cable to do uploading and you have to use the same port for MIDI so you can't easily get serial debug output. The Arduino Nano has an on-board USB-to-Serial adapter so you don't need an external one but that adapter uses the only hardware serial port so, again, you have to use the same port for MIDI so you can't easily get serial debug output.