You don't say what radio the multi-section cap is out of, but it seems to consist of one 40uF cap, two 30uF caps (all 160VW) and a 25uF 25VW cap. It's reasonable to assume that one (probably 40uF) is the reservoir cap - the first one after the rectified HT - the two 30uF caps are for smoothing, and given its low working voltage, the 25uF one is a cathode bypass capacitor, maybe in the audio stage. The usual colour code for electrolytics was that red denoted the outer foil and was the reservoir capacitor, which has to work the hardest, so by making that the outer cap would get best cooling. Red was the smoothing cap, and black was ground.
How you empty the existing cap depends on the nature of the filler which seal the caps (which will be wound concentrically) into the case. It may be hard wax, pitch or some other substance. Whatever it is will have a bearing on whether it can be heated up sufficiently to enable you to withdraw the contents without damaging the case. If you can't, the other option would be to use something like a Forstner bit at slow speed in a pillar drill with the cap held in your hand. That way, if the drill bit catches, the cap will spin round, whereas if you had it in a drill vice, it could be snatched out and damaged.
Having emptied the innards of the old cap, when it comes to re-stuffing the capacitors, the best choice in my view would be Rubycon miniature capacitors as stocked by Farnell. When used in smoothing circuits, capacitors need to have a high ripple rating and not all of them do have - it's often not stated. Despite their small size, Rubycons do have a high ripple rating, as their datasheet shows.
You may already understand the significance of the ripple rating of reservoir/smoothing caps, but in case you don't, the diagrams below might be of interest. Pic 1 shows a full wave rectified smoothing circuit, pic 2 shows half wave rectification, and the third pic is of the smoothing circuit of a typical radio - a Portadyne A33.
The fourth pic shows a selection of Rubycon miniature electrolytic caps.
At first sight they look puny and not up to the task, but they have high ripple ratings beyond what's needed for typical domestic valve radios. Those in the attached picture from left to right in the 'front row' are 15uF, 22uF, 33uF and 47uF. The three between the two cans are 18uF and give an indication of their small size. The small can on the left is a (NOS) 3-section 16uF which is 25mm diam x 45mm tall (1" x 1.75" in 'old money). The yellow can on the right is a (NOS) 2 section 16uF which is 35mm diam x 50mm tall. (1.5" x 2") - same size as the smoothing/reservoir cap in the DAC90A etc. As can be seen, even in the smaller can, three caps would just fit side by side, 'triangular fashion'.
Rubycon caps from Farnell aren't expensive and they have a good range:
https://uk.farnell.com/search?st=Rub...c%20capacitors
The datasheet giving dimensions and ripple ratings can be found here:
http://www.farnell.com/datasheets/23...EaAkhnEALw_wcB
As the 25uF one in your multi-section cap is only 25V, it will be quite small (no thicker than a pencil and about 2.5cm long) and if it's a cathode bypass cap, ripple rating is irrelevant. A 22uF 35V Rubycon would only be 5mm diam x 11mm long.
For replacements, use the modern values: For 30uF use 33uF, for 40uF use 47uF and for 25uF, use 22uF. Depending on the dimensions of the empty case, you might need to use 'squat' caps one above each other, or might get three long slim ones side by side. If you were to use 160 VW ones again, Rubycon 22uF would only be 10mm x 12.5mm and 33uF would only be 10mm x 16mm. Even 250V ones would only be 10mm x 16mm & 10mm x 20mm.
To terminate the caps, all the negative leads can be commoned to a black lead as they are now, then you can use the same colour code as before for the positive connections. Personally, I'd use silicone flex for the leads, as sold by forum member Phil Marrison, 'SWB 18' to whom you could send a PM. I'd seal the end of the tube with 2-part epoxy known as 'Super Steel' which - despite its name, isn't electrically conductive and is black when cured, looking rather like pitch.
The last pic is of a small twin-unit can type electrolytic capacitor which I re-stuffed in a Unitra 'Figaro Special' using miniature caps.
I hope these rather wordy notes are of interest and relevance.