You could be right. It is quite possible that the inputs are turned into a positive and negative rail. So you might need a +21V battery and a -21V battery.
Indeed, and unless one were prepared to risk pure trial and error, I don't think that one would/could know whether that were the case (or which way around to connect the batteries) without opening it up (and 'having some knowledge').
All seems a bit over the top for typical audio circuitry, though having positive and negative internal rails for the op-amps is, in itself, beneficial.
I agree - and, even if one wants positive/negative rails, as I said before it is very odd/unusual (at least in my experience) to have two out-of-phase ELV AC inputs into something which is presumably just very low power electronics.
I probably misunderstood your 'taking it apart', by which I guess now you meant 'opening it up'. I thought you were suggesting re-working the circuit, and was just pointing out that it was likely not to be necessary.
Yes, 'opening it up for a look' (with an understanding of what one would looking at) was what I primarily meant. It could be more complicated than we are envisioning. Given that what's going in is AC, it's even not impossible that there are other ('true') transformer(s) inside - e.g. to provide a separate 5V supply as well as, say, +/- 15V rails (something which would obviously fail to work if one had fed DC into the 'AC inputs'). That's another reason that I would want 'a good look inside'!
For the benefit of the OP however, batteries may be an option, and it may not require any modification to the unit, but would probably require 2 x 21V batteries.
Yes, it certainly is a theoretical option(i.e.
must be possible, even if modification to unit were required), and
may well be possible without modification to the unit. However, even if it were adequate (via the input socket) "2 x 21V batteries" would raise issues. Unless one built the batteries oneself with individual cells, it might well end up as 2 x 24V batteries - and that could raise issues that required some attention.
Kind Regards, John