Since you have them, there's certainly no harm in putting the 10's in there. The 4.7 would be off a bit anyway (only 6% assuming all the caps are spot on, which they never are). In view of the comment above about the quality of parts, definitely remove the old ones carefully and save them. If you have a meter that will test caps, it would be interesting to see how they measure out. And if you can do that, you can also mix and match up the new 10's to get values for each speaker that are the closest to each other.
If you want to verify your crossover drawing while the speaker is open for the cap replacement, one way you can do that is just to trace from + and - on each driver back toward the inputs and verify that everything is connected in the order shown on the drawings. Wouldn't hurt to add in the switches and wiring also. Or, if you can get more pics showing all the wiring, we might be able to tease it out from the photos. Right now the photos are from too far away to be useful for that. It's mainly for documentation purposes since there is nothing on the net on these, so it's up to you how much time you want to put into it. But I'd be willing to take another crack at a schematic given some more info to work with. Just in the name of science.