"Does a file have to exist ...?"

The Zen answer: Can you open a paper bag if you don't have a bag?"

Actually, Perl is somewhat less rigid about that: The answer lies in your terminal: perldoc -f open.

As to your line 26 and title: you seem to have an odd spec: you talk about hex but present octal values....

and those appear to be:

\000-\011\013\014\016-\037
 NUL  TAB  VT FF   SO   US
[download]

or, if interpreted as hex:

 NUL  DC1  DC3   DC4    SYN   Digit-'7'

Are you sure you've identified the chars you wish to remove correctly?