There is a reproduction cardboard can electrolytic with new caps in it which will work much better as a replacement...I dont think those types of electrolytics you have got will fit in there, there is just not enough room.
You can get the replacement caps at
http://www.tubesandmore.com
Click on "capacitors" and "multi and single section tubular electrolytics"
The site uses frames so there is no way to link right to the caps.
I think those needle nose are too big for this job...you need a type like an Xcelite which is made for electronic work.