No, you can't.
The Wallets RPC - Interface opens the connection only after opening the wallet and its lifetime is completely dependant on the wallet. If you close a wallet, it will shut down the RPC interface as well. This is caused by the design of a wallet instead of a dynamic daemon.
Your described problem with a visible password when listing the running processes is known and has been discussed already. While it is faster for an attacker to just read the password from the window title, your wallet is compromised anyways as soon as an attacker has access to your computer. This cannot be stopped by encrypting a connection or not having the password in the window title, as he would be able to read the password from your computers memory, trick you into entering it again, running a keylogger etc.
While a possible attacker in your network could sniff your user-agent, this wouldn't be much use to him as he can't modify your browser user agent to perform the CSRF attack the user-agent was established against. Keep in mind that the user-agent is not a password protection and trying to protect a public wallet in RPC mode like this will lead to a compromise by anybody who can take a look at your connection to it. The user-agent is only a temporary solution against CSRF, a more secure solution is worked upon (since some time, the priority is considered very low due to the very limited attack opportunities).