DFT for audio classification - signals of different lengths
As you explicitly mention, that you are aware of a loss of information and are willing to accept that, a possible solution will be modulo-N reduction or wrapping, as described by Orfanidis in the freely available book "Introduction to Signal Processing" on pages 489ff.

In modulo-$N$ reduction, a vector $x$ with length $L &gt; N$, where $N$ is the DFT length, is divided into non-overlapping blocks of length $N$. These blocks are summed up, resulting in one vector $\tilde{x}$ of length $N$ .


Figure taken from Orfanidis (linked above), Fig. 9.5.1 on page 489.

You then apply the DFT on $\tilde{x}$, which results in $\tilde{X} = \text{DFT}\{ \tilde{x} \}$ with length $N$. Orfanidis proves that $\tilde{X}$ is exactly equal to the $N$-point DFT of $x$, so is equal to $X$.

In your case, that would mean you could find a minimal length $N$, which is guaranteed for all input signals. You then apply a modulo-$N$ reduction on all your input signals and compare these length-$N$ DFTs. Of course, a higher resolution would be possible for longer signals, and you just ignore this by using the modulo-$N$ reduction method.

Similarly, you could just zero-pad all signals to a maximal length $M$. All your signals will then have a high frequency resolution defined by $M$. Important point: you do have that computational frequency resolution, but the physical frequency resolution is still determined by the length of your signals $L$. More details on this are given in any decent signal processing class or on pages 482ff in Orfanidis.