the problem with measuring with the computer is the variance of adding a converter in the circuit will give inaccurate results. Audio converters are not electronic lab/instrumentation grade in their coupling. So you would get what is capable for that signal chain.
Well, since you don't HAVE lab/instrumentation grade kit, do the best with what you have! A decent modern AI will give a noise floor of better than -100dBFS, I doubt the mic pre will get close to that.
Were you UK based I would loan you my Wayne/Kerr/Radford microvoltmeter, gladly!