Yes, you can replace just the rope in the recoil, and it will work great. The only thing you have to do after you get the new rope in and wound around the spool is pre-load the spring. You do this by turning the spool clockwise 2 to 3 revolutions, then tie the rubber handle on the end of the rope after it is through the hole in the recoil case. Make sure to spray some wd 40 on all the parts in there, it looks like it needs it.
THE 80's RAGE! Currently owns:
81, 85 Yamaha Tri Moto 125
83 Yamaha Tri Moto 200 x2
82,83 Yamaha Tri Moto 175 project
85 Yamaha Tri Z 250
84 Kawasaki Tecate 250
84 Honda ATC 70
85 Honda ATC 350X
84 Honda ATC 250R
(2) 84 Honda ATC 200x
82, 83 Honda ATC 185s
81 ATC 200
Lots of other parts and bikes