Good work. I have a couple of radios with the odd cap that was so buried, I had to remove multiple components to gain access.
In cases where the tiniest snipper wouldn't fit, I have used an X-acto tool with a little razor saw to cut the old leads, and a forceps to work the old cap out of its burrow. At some hobby store, I also found a soldering iron that's thinner and longer than most. Fairly low wattage, but useful in these cases.
Some times an orange drop is too chubby to fit in the old space. The "little yellow" capacitors work just as well and are much smaller.
Phil Nelson
Phil's Old Radios
http://antiqueradio.org/index.html