"When I enter https://papercut:9192/ there is a SCARY warning sign. What should I do? Is it secure?"
Yes it is secure, just proceed.
The purpose of using a "https" instead of "http" is to provide a secure connection (a.k.a SSL connection) from your browser to papercut server. i.e. when you enter your username and password on browser, all information are encrypted and it cannot be read in clear directly off the network ("sniffing" as the hacker call it).
This secure connections is provided by papercut server used a self-signed certificate which work exactly like a certificate used by the gmail, yahoo or your bank, EXCEPT that they are NOT signed by a known Certificate Authority so the self-signed certificate cause the Browsers to raise the red-flag.
Click "Proceed anyway".
Click "I understand the Risks".