I'm going to guess you can't measure it over the room noise even if you can hear it over the room noise.
You might be able to calibrate your regular microphone... I assume you have a mic and an interface and some digital recording software that can give you digital levels... Run some white noise and get an SPL reading and a digital dBFS reading at the same time. Then for example, if the SPL reading drops by 6dB the digital level will also drop by 6dB.
There are a couple of issues with that - When you measure the real hiss the levels will be very low and those may be swamped by preamp noise and/or room noise. (Of course you'll have to amplify digitally but as long as you know how much you are amplifying you can stay calibrated.)
And your microphone-digital readings are not weighted. That might not be a big deal since hiss is similar to white noise, or you could high-pass filter your generated white noise to better-approximate the characteristics of the hiss from the tweeter.
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...I've got an older analog Radio Shack SPL meter with a dial with a few ranges to choose from, but I'm pretty sure it also couldn't measure that low-level hiss. I just ordered a cheap ~$100 SPL calibrator for it because I've read that electret condenser mics loose their sensitivity over time (like old people
). I could have bought a new cheap SPL meter but I thought it would be more fun to have the calibrator. They claim it's accurate to 0.3dB (at 1kHz and 94dB SPL) but at that price it's not certified or calibrated by an independent lab so I don't really believe it.