If you don't feel good about it, don't do it. What are you going to lose? $15? The thing with a very old wrap is that you have no idea how it's installed (if it's done well you often cannot tell if it's tucked or drilled until you remove it), nor do you know what adhesive is under it. If it's white glue then you might find it giving out when you decide to drench it with solvent. If it's yellow glue you might be alright. But how do you know? And what if it's dry rotted? Have you ever cleaned a wrap with a razor blade? Works wonders and no solvents or detergents are needed, BUT disaster if the wrap is dry rotted. These things are "experience" based knowledge that come with time and experience. If you are not experienced enough to assess the situation then don't be afraid to tell your customer that you are unsure of what the outcome would be if you proceed, so it would be best if you didn't. He should respect & understand that you know your own limitations and are looking out for his behalf.
There's nothing wrong with inexperience or not knowing what to do. It's an opportunity to learn. If it were me, i'd offer to give it a shot & if I failed then a free rewrap. If he's ok with that then you have free reign to experiment & learn. Try different methods of cleaning and give the razor blade scrape technique a shot. So what if you screw up. You just learned an invaluable lesson for the cost of some linen, and still have a happy customer. Of course if the wrap is sentimental or worth something to him, then by all means don't touch it. But if he's just being a likely cheapo, then both of you win. Something to find out before you begin. But don't ever be afraid or ashamed of not knowing something. It's an opportunity to learn. And learning those lessons make you better. Letting this guy go might cost you some valuable knowledge & experience that are worth far more than the price you charge for a rewrap. How do you think anybody else learned? We weren't born knowing how to do this stuff. I can't count on all my fingers & toes how many times I made deals with cheapo players on repair work, just so I could learn. A lot of times it meant doing work for free, or fixing something I never intended on fixing. But I learned & that was worth more than the price I charge for repairs. I learned how other cues are built, where they commonly fail, when to accept jobs & when to pass. One time I took a rewrap job & once the old wrap was removed, the entire butt sleeve with cap and rings all fell off the cue. I learned how to fix that and something to look for in every other cue that comes for rewraps. Don't be scared. Make him a deal. You'll be the one getting the better deal in knowledge, while he'll be happy he's getting the work done cheap or free. Just be honest with him about it & see how it goes.