This might work but sending cash in the mail is a pretty terrible idea. Most postal services strongly discourage it, or you're using recorded services which are expensive and add all the same tracking issues.
https://www.wusa9.com/article/news/verify/can-you-send-cash-...
https://apnews.com/article/archive-fact-checking-9264421609
You should report to the postmaster general if you are refused service; they would be interested in hearing about this.
https://faq.usps.com/s/article/What-are-the-Limits-for-Insur...
I found this out the hard way trying to overnight about $500 cash to a family member.