Well, the two things i would upgrade on a Shutter would be the barrel, the grip frame, and the expansion chamber. The order in which you get these depends on if you are after a faster fire rate or more accuracy, or more consistent chronoing.
It also depends on how much cash you wanna get rid of, the cheapest option i think would be to go for a DYE Excel barrel or something similar for around £35, and it's a pretty decent barrel.
Or if you feel like spending more, get a boomstick, one of the best out there for about £80.......or you could get an electronic grip frame for about £100 which would give you a light trigger pull of as little as 1mm. Oh yeah, almost forgot the expansion chamber. The shutter only has a 2 or 3 stage one, i would invest in a 6 stage expansion chamber for more consistent velocities, especially if you run on CO2. You can pick up a 6 stage expansion chamber for less than £25.