Most white noise sources I've seen are a rather simple source with one or two LNA stages. So making my own LNA could go right into the white noise source. So step one is to get an LNA. I've reviewed a couple and it seems the LNA4ALL is very popular. It's a good solution for $20. However, it really needs to have the case which adds a significant cost ($60). So I've decided to design my own customized LNA based on the LNA4ALL.
I've found a housing that I believe will work well. It's about $8 which is way lower than $60. However, this would mean I would have to feed DC power up the line. But the RTL-SDR has a provision for that with a build-in bias-T. I can solder a jumper to the RTL-SDR to get ~4.5V DC up the wire.
I believe I can fit a circuit board inside this housing with an LNA on it. For sure it will be a tight fit to get a PCB in there with everything I need but I believe it can be done. The shield will slide over the top of it providing a good ground and EMI/ESD protection. Next step is to figure out how much space I actually have to cram circuits in there.