Following a reference to Darley et al., ApJ 746, 61 (2012) from your Wikipedia link gives a (very technical) discussion of nova progenitors, including distinctions between nova systems where the secondary stars are main sequence or supergiant stars, and distinctions among white dwarfs with different chemistries.
The first sentence of that paper is
A classical nova (CN) outburst occurs in an interacting
binary system comprising a white dwarf (WD, the primary) and
typically a late-type main-sequence (MS) star (the secondary)
that fills its Roche lobe (Crawford & Kraft, 1956).
That suggests the 1956 paper is the original proposal for the Roche overflow model of the classical nova.
Like many original-idea papers, it's a pretty clear read.
But for your question, Crawford and Kraft seem to hedge about whether the "blue star" in their particular pair needs to be a white dwarf:
In other words, Crawford and Kraft don't come out and say "definitely a WD," but if it's a non-degenerate star, it's a very strange one.
More modern observations of novae are compared to detailed models of the dynamics of the surface dynamics, models which have been debated vigorously for decades; the current generation of comparisons to data are sensitive to details like the amount of helium accumulating on the white dwarf's surface during the nova event. It seems unlikely that such details could even come close if the underlying assumptions about the basic physics of the erupting star were wrong.
Note that a classical nova system can be thought of as a type of contact binary star.
For any reasonable estimate of the size of the giant star, a distance of 10 AU between the two members of the pair seems like an overlarge estimate.
Ten astronomical units of separation viewed from a distance of 50 parsecs is already a gap of 0.1 seconds of arc. I wouldn't expect to see visible-light photographs showing both the giant star and the white dwarf, but rather that all of the information about the binary systems comes from spectroscopy.