Well, you might want to take a look
here for sunlight wavelengts, and also
here for technical specs of glass. Don't worry, it's only some curves. Which show you that UVC really doesn't play a role...
That raises your shortest relevant wavelength to >250nm... ...quite a bit of which, however, is still absorbed by standard bulk glass. And makes the standard digicam CMOS sensors somewhat adequate (they still have weaknesses in the UV range). So, apart from the optics, you'll get away cheaply.
Spectroscope building kits are available from 5€-ish, like
this DIY cardboard kit. Take a look at the third image in the first half's link to see what you'd get. Or for a bit more (<20€) you can get
e.g. this handheld hobby spectroscope, which, again, will probably only work the visual range. Also, they only give you a spectrum, no quantitative measurement, nor full sky view.
You can pimp that up for some with an affordable ocular cam like
this one here. The linked one has a built-in UV/IR filter. Getting to the data for those parts of the spectrum, though, might hence be possible, by just removing the filters. This setup would be semi-quantitative... ...but you might have to experiment quite a bit with how this is displayed, by adjusting the distance between your diffraction grate and the cam. Maybe even find some computer savvy person to read those data. Also, you probably won't get any precise wavelength for your measurements.
But... ...if you're into an
art project, this might even be better. Colorful spectra should be quite the eye-catcher!
So the question you'd have to answer is: Can you live with a qualitative display - od do you really need to quantify your light intensities?
Keep in mind that much of the light absorption due to cloud cover is in the IR range (which you can see in the very first link in this post). And there actually are some Bio/Med/Psych papers proposing / finding that this really does influence people's mood...
Also be aware that the sunshine and exposure duration are relevant for mood, too. So the daylight & sunshine hours, and the time your "test subjects" spend outdoors will have to be figured into your analysis, too.
Disclaimer:
The links are
not intended to advertise specific products, by a specific manufacturer, or via a specific retailer! They're merely meant as examples to illustrate what the market does offer.
Should that violate the forum rules, I'll immediately remove them.