Timing and rhythm
Songs can be useful for (imprecisely) measuring lengths of time, either through the length of the entire song, or through its tempo. Planetside, there are a number of song-based timing techniques, such as washing your hands while singinglong enough to sing "Happy Birthday" twice, or performing CPR to the beat of "Stayin' Alive".
It's reasonable to think that a space shanty could be used as an easy way to remember the timing of common tasks. Perhaps you need to manually prime some rocket fuel pump not-too-fast but not-too-slow, so doing it to the beat of a sea shanty is just right. Maybe you need to wait for a system to cool off after shutting it down before performing maintenance, so singing a couple of verses will help keep you from burning yourself. Humming a song in your head can also be a rough measure of time if a clock is unavailable - if you finish humming the entire shanty, you had better wrapfinish your spacewalk no matter what your oxygen gauge reads. I'm envisioning these techniques as being particularly useful in a spacepunk-esque setting with rust-bucket spaceships, where computerized control of timing is either unavailable or unreliable.
Sea shanties are typically sung in groups, but it could still be useful to have a common song that all crew members sing even individually, to provide consistency as different people perform different tasks. Even if the song is usually sung individually, it can still provide consistency and cohesion across the group. Of course, any song with the right tempo and length could be used for these purposes, but a shanty is a nice thematic fit.