From your project description, I assume that you have some knowledge of analog electronics. So you should be able to understand the comments about missing AC coupling in your Z-diode noise generator. Also the Z-diode must have a suitable zener voltage within supply range, e.g. 5.6 or 6.8V, C27 can't work. But the circuit should work generally. The zener-diode supply voltage should have a good filtering, for low frequency noise, an ausxilary voltage regulator may be meaningful.
I have used similar noise generators for audio purposes. A digital LFSR (pseudo random) noise source can be used as well, it shows a periodic sequence of a defined length, e.g. 10 sec.. This property can be a disadvantage for measurements that require true randomness but may be an advantage for others.