If you can manage 25 miles (40km) regularly, you can almost certainly manage 102km as a one-off event. And between now and then, you've got plenty of opportunity to increase your mileage anyway. As
@I like Skol says, you will get carried away by the sense of occasion and achieve more on an event surrounded by lots of other cyclists than you could on a solo ride.
One caveat I would add is that if you're not used to riding in big bunches, it's worth getting some practice in - in fact, this is just as important as being able to cover the distance. Ideally, find a local club to ride with - that doesn't mean you have to ride with the fast racing types, many clubs organise more moderately paced, sociable rides too. You might ride the sportive as a solo entrant but you will be surrounded by lots of other riders, so it's as well to learn some group riding etiquette. Also sportives often attract a portion of idiots who treat it as a race with no regard for other riders, so if you learn to be confident around large groups, you'll be in a better position to look out for your own safety when you encounter these types.
There's nothing wrong with using a hybrid on a sportive, but the big advantage of a road bike is the drop handlebars, which give you a variety of hand positions (better for comfort on long rides) and allow you to get into a more aerodynamic riding position, therefore faster for the same level of effort. From what you say about your hand comfort problems, you may find drop bars a real benefit. Getting a full bike fit can help with comfort too - many problems are caused by not having the bike set up properly.
I don't know of any specific rules about bar ends on sportives but a lot of events ban aero bars on mass-start events for safety reasons, so bar ends may fall into the same category (it's having pointy bits sticking out of the front of your bike that is considered a problem). (ETA: cross-posted with
@Pale Rider )
