That those caps are of multiple different manufacture means utterly nothing as far their being original or replacements. There was no "directive" or "design objective" in place at the time these amps were manufactured that "all caps should be by the same manufacturer". The maker simply went into the market to his several suppliers and bought his .02 caps as cheaply as he could and bought his .1 caps as cheaply as he could and if one was this brand and one was another brand it was of utterly zero concern. Some time back, someone posted a gut shot of an amp that had EIGHT different manufacturers of non-electrolytic caps! Maybe the maker of the amp got a super deal on .02's a year or two earlier (for a different model amp) then he ran out of .05's and had to go buy them much later than he bought the .02's.
I would suggest a slightly different though not exclusive approach. Examine the solder joints carefully, with a magnifying glass. If some are of a distinctly different patina than others, the shinier ones are probably replacements. Most coupling caps and small value non-electrolytic caps in an otherwise unmessed-with 50's-60's amp have very long lives are most likely original. It's entirely common to find Fender amps with all their original Ajax blue-molded caps. On the other hand, the black striped "bumble-bee" caps are known to be leakers.
I can understand the desirability of having a schematic and I completely agree. And, I would exhaust every avenue of internet forums and spend plenty of time searching before proceeding without one...but one is not absolutely needed if you just replace one part at a time. This of course depends upon your understanding of tube amps in general and, for example, being able to realize that the little tubes are preamp and tremolo tubes and in the great majority of cases they have about 100K plate resistors and 1-2K cathode resistors, and a 12AX7 has this/these pin(s) as the plate(s) and these two are the cathodes.
It all depends upon how much time you are willing to invest. Drawing a schematic from a circuit in front of you is a pretty tedious job, IMO. And there are no guarantees you won't get something wrong with that.