First: don't worry about the "a cappella", sea shanties are ALWAYS sung a cappella, although not necessarily in the style of chapel or church music.
Second: sing as if there will be a large tot of dark rum waiting for you at the end of your shift.
Third: there are approximately 1,532,378 sea shanties available in this world, sing all of them.
Fourth: keep on singing, you are certainly no worse than many of us who sing sea shanties in the shower, and think we're sailors.
Dim ond yn cadw ar ganu, frawd.