There is no historical data on the Sun's output in even the visible part of spectrum, let alone UV or IR, prior to the 20th century. Back then astronomers could only count sunspots, and only relatively recently.
If the "climate scientist" allows the Sun into his equations then he has no equations, and no money, and no influence. You can't build a theory of something if the most important factor in that theory is one big unknown for most of the time.
The issue is not measurements, but Planck's Law, which describes the spectrum, and was published in 1900. Once that law is known, the relationship between changes in total solar output and solar output in the UV are clear. A minor rise in temperature, that shifts the peak wavelength only slightly toward the short wavelengths, will cause a proportionately much greater increase in UV output. That's why I say no scientist should be surprised that there's a lot of variability in the sun's UV output. On the short wavelength end, Planck's law is very sensitive to minor changes in temperature.