You don't even have to take out the crossover. Just pull the horn, and you'll have plenty of space to work with. I found it helpful to drop in an automotive trouble (work) light into the cabinet so I could better see what I was doing.
The black Altec caps have the values clearly marked on them. When you're ready to replace them you can unsolder one leg at a time (and even solder in the new cap in its place to avoid miss-locating it); or draw a simple diagram to remind you where things go.
You might find it an interesting exercise to do one box first, and then hook them back up to your stereo and do an A_B comparison with the balance control. I did that, and then invited family members in to offer opinions. They unanimously preferred the new caps.
You can pick up Solen caps at http://www.madisound.com
Good luck.