All I have on hand is a 40W tip and a Weller WES51 (50W). I plan to work for about 8 hours. Can I do any major damage to the iron or the work?
What you are asking makes no sense. We have several Weller WES51 around here, so I am quite familiar with them. The tips don't have a power rating. The difference between the tips is the shape. For example, the ETP tip is good for most general work, and is listed as being ".8mm conical". The ETT tip is ".61mm conical" and comes to a slightly finer point.
These tips are just metal. The heater and temperature feedback are in the iron. All the tips have the same mechanical interface on the iron side. There is no such thing as a "40 W" tip.
If the tip you have fits mechanically into the PES51 iron, then I'd say give it a try. As long as the fit is good, the iron should regulate the temperature well enough. Also, wattage of a temperature controlled iron only tells you the maximum it is capable of, which should be rather more than you actually use on average so that the temperature controller has some extra to work with.
Ratings are typically lower than capabilities by a margin of safety. For this reason alone I would say using the tip should be fine. The only way to know for sure is to contact Weller.
As for whether you can damage the iron or the work--I would expect the iron to survive fine, and damage to the work depends on your soldering skills. I can't imagine any more possibility for error than poking at your device with a multi-hundred-degree tool for 8 hours, though. =]