Depends. If you're on a trainer you can swap while leaving the old bars dangling. This is how I checked out a few different bar/stem combos (I had to change the stem due to different bar reach/drop dimensions).

If your cables/housing were optimized for the 38 cm bars then by definition they'll be too short for 40 cm bars. You shouldn't be able to turn the bars all the way with a 40 cm bar for example.

However if the fitter/installer gave you a bit of room to adjust things like height or bar width then the cables/housing should be cut a bit long. Then you can swap without much problem. Unwrap the bar tape, slice the electrical tape holding the housing in place, loosen levers, remove bar, then reverse the steps for the other bar.

Personally I'd leave the bars unwrapped for the first hour or two or riding, even outside. I usually test on the trainer though, with a final test outside. You can fiddle with lever height/placement, swap bars back, etc.

If there's no problems with cable/housing length then it won't take long to swap the bars (without wrapping with tape), maybe 10 minutes of real time, 5 minutes if you rush it.

If you have Nokon cable housing then you can "grow" the housing, i.e. if the housing was optimized for 38 cm bars then you can add segments for the 40 cm bar. I use Nokons partially for this reason. The different bars I've checked out have massively different housing length requirements and by simply adding/removing segments I can adjust the length.

As others have pointed out handlebar width is a personal preference, it's one step less personal than saddle choice. Only you can decide the best compromise between the different widths. You haven't even addressed the bar shape which is even more variable!

For me personally I could use a 44 cm bar based on my shoulder width; I tried and decided against a 46 cm. People on BF have asked if I was using a 38 cm bar after seeing pictures of me in the sprint. I use either a 41 or 42 cm bar. I like this range of width because it works in a tight group for feeling like I can squeeze through gaps (1 cm on each side doesn't seem like much but it's like a few inches width on a car - doesn't seem like much until you're squeezing past another vehicle). I also prefer a narrower bar for out of the saddle sprinting.

When I trained outside more in the off season I'd actually switch to a 42-43 cm bar. I felt it was more comfortable for the easy/steady rides I did, a lot of time spent on the tops. When spring rolled around I'd switch back.

Good luck with the bars,
cdr