You cannot use WSPR to check harmonics. What I mean is, you cannot transmit WSPR on 80m, on a frequency adjusted so that the 2nd harmonic falls in the 40m WSPR sub-band.
The reason why this won't work is the tone-spacing will be doubled. WSPR consists of 4 tones spaced 1.46Hz. At the 2nd harmonic, everything will be doubled: including the tone spacing. So there will never be any WSPR decodes of any harmonics.
Concluding there is no energy at the harmonics, because are never any WSPR receptions at the harmonics, would be false.
73 Hans G0UPL