Shotblasting?

Polish instead

Don't need to do anything (light oil afterward perhaps ...), but a ceramic coat might not only help with longevity, but they will remain cleaner over time.

I ceramic coated a set on my old 06. On the whole it lasted well but around the front and rear downpipe they still started to look a bit like that. I guess if you don't ride in the wet and cleaned that are after every ride it might help them stay a bit cleaner.

Personally I would get them blasted and then use a light oil as suggested. Can always clean them with some wire wool if they start to get encrusted with shit again.

Most shot blast finishes are relatively rough and will pick up dirt quickly and be hard to clean. Best to polish the surface after blasting in my experience. Rotary wire brush followed by buffing wheel in power drill will do it. Are the pipes steel, stainless or titanium? You don't say.

Enquire about ice, CO2 or other less abrasive blasting options, shot or bead blasting will make a mess of them.

If you want them to shine consider caustic dipping to remove the coating followed by pickling to bring the metal back to shiny, assuming they're stainless steel.

Agreed avoid shotblasting it can be too agressive, glass beads may be ok but leave a satin finish.
In addition any iron in the shot or beads (cross contamination) can embed in the stainless and cause rust spots and stains in the future.

What about aquablasting, not quite so abrasive. Works well on alloys not sure on stainless.