You can use the same chords if you are just playing the chords as arpeggios. However, if you are saying that you want to play the melody instead of singing it, then that's a whole different issue.
The melody or at least, the bare bones, can be found in the chords. I learn many melodies like this. Find the starting note and peck and poke at the melody. Once you have the basic line you can move outside the triad.
even if you're not interested in playing any melody line sussed out from the basic chords, you can always play finger picked arpeggios of the same chords instead of strumming them.