First of all, do you know how they were attached Plastic glue will melt the two bits together, meaning you can only separate them by cutting/sawing through. If the bits were superglued, put them in the freezer and hope he glue beomes brittle enough that you can tear the bits loose.
1. If you have a spare bike handle, just cut it off. If not, do you have the right diameter plastic tubing or alternative to make a new handle?
2. Hope it was superglued and not put together with plastic cement

. If you have a dremel, remove as much as possible with a cutting disk, then grind the rest down. Removing the fairing this way is pretty invasive surgery, be aware you could lose the patient.