It turned out that configuring my own forward HTTP proxy was actually really simple! Here's how I did it. First, I placed the following nginx configuration file in /etc/nginx/sites-enabled/
:
server {
listen 81;
location / {
resolver 8.8.8.8;
proxy_http_version 1.1;
proxy_pass https://$host$request_uri;
}
}
Then, on the Window 95 machine, I opened Netscape Communicator and went to Edit -> Preferences -> Advanced -> Proxies -> Manual Proxy Configuration
and entered the following information:

(Note that 192.168.178.129
is the IP address of the machine that is running nginx in my case.)
That's it! Netscape Communicator now happily connects to any HTTPS website. As proof, here is a screenshot of this very question, as rendered by this 25 year old web browser:
