The only thing he cannot do is feed baby. I wouldn't introduce bottle for that reason. Also baby will soon grow up and stay awake for longer, start "playing" etc. This newborn phase doesn't last very long x
My husband loves a contact nap but he struggled with our first when he was a newborn too, he’s 3 years old now and they are the best of friends! He may feel a bit unhelpful right now but there will be loads of fun things they can do as baby gets older
How about doing tummy time/play time or contact naps? He could also do skin to skin?