The absence of insulation by itself will not cause lack of spark. What will cause a problem is (a) if the bare wire makes contact with (shorts to) grounded metal or other bare wires, or (b) if the wire is corroded so badly that it's cross-sectional area is reduced so that the wire's resistance is significantly high or it's connection to a crimp terminal is corroded or loose causing a high resistance connection.
I don't have a 1st gen. FSM/wiring diagram. Download it and see what that wire is. If it's a ground wire, should be no problem, otherwise probably would be a problem: 1st Gen FSM Factory Service Manual
There's no Light Green/Black stripe wire on the ASD relay. There is Dark Green/Black Stripe wire on the Fuel Pump relay according to the diagram below. Are you sure you're referencing the correct relay? And if that wire is grounding out then the fuel pump wouldn't run and probably blew a fuse. Fuse A 20a in the Power Distribution Center under the hood.
There are Light Green/Black stripe wires that are Voltage feeds to the EGR Solenoid, Manifold Tuning Valve and Evap Purge Solenoid.
The wires for the Ignition Coil and Fuel Injectors is a Dark Green/Orange Stripe wire from the ASD relay.
I would make sure that all of your fuses in the Power Distribution Center under the hood and in the Junction Block at the end of the Dashboard are good. They need to be verified with a Multimeter and not just visually checked. They may "Look Good" but still be open.
97 asd relay has a dark green/orange wire coming that's power, and a dk blue/yellow control. red/white powers the other side of both.
light green/black i can find powers the egr, mtv, and evap purge solenoid.
not likely to cause a spark problem.