That was my first thought but can dolphins breathe out of their mouths?
*Searching say no. Can I say duckduckgoing? Ducking? Ducking says no. Separate breathing and feeding tubes. We should do that.
**More ducking says "Until recently it was thought that dolphins could not breathe through their mouths in the same way as people can, only through their blowholes. However, in 2016 scientists discovered a New Zealand dolphin with a damaged blowhole who had learnt to breathe through his or her mouth."
*What do you reckon the past participle would be? Google/Googled is easy. Duckduckgoed sounds wrong. Duckduckwent is probably correct. Ducked might be easily misinterpreted/misunderstood.
Unlike most of these sorts of things, this one has a definite answer: 2. They cannot blow air out of their mouths. However, since they have no hands to work the valves, it wouldn't sound too good, assuming they could get it to stay in place to begin with.
Valves aren't needed to "sound too good", they're needed to get more notes. Without valves, you've still got the harmonic series. Any piece played on bugle could also be played on trumpet. And the majority of classical compositions up until the late 19th century. (All classical compositions until the early 19th century.)
Your lips do important work in making a trumpet play. Dolphins don't have the fine control over their lips that would be necessary. Maybe the blowhole does?
No, they are unable to breathe through their mouths at all. Their respiratory system is bonkers compared to other mammals. Their blowhole is one nostril,which is used for breathing , while the other nostril is located in their skull and is used for echolocation and vocalizations.
A dolphin would likely play something more like a trombone with an articulating system of pipes that could be played through vigorous contortions of the body. Think playing a trombone but with a hula hooping/swimming motion. Perhaps a small lever could extend out to the dolphin flipper that would allow nuanced fine pitch control with lateral contortions of the dolphin’s flipper.