You may need to take the pull start cassette off to see how the rope terminates (which you need to do anyway to replace it, so might as well go ahead and do that now), which will determine if a stiffer rope will work if it needs knotted or kinked sharply, but otherwise yes you can use just about anything that is reasonably abrasion resistant.
I'd estimate a typical cord is about 5/32" diameter or if coming from overseas, might really be 4mm, though I could be overestimating and it's really 3mm or 1/8". You should be able to look at the grommet it passes through and the cassette track to see what max diameter will fit... the pull handle too though it would be easiest to enlarge its hole if needed.