Actually I think that the menu command as provided always wraps at 80 regardless of what your wrap is currently set to.
In any case, if you’re going to do the same thing on a regular basis, you can perhaps get away with a macro. For example, if you save the following as Packages\User\RewrapAndQuote.sublime-macro
:
[
{ "command": "select_all"},
{ "command": "wrap_lines", "args": {"width": 78 } },
{ "command": "select_all"},
{ "command": "split_selection_into_lines"},
{ "command": "move_to", "args": {"extend": false, "to": "bol"} },
{ "command": "insert", "args": {"characters": "> "} },
{ "command": "single_selection"}
]
You can execute it from the menu via Tools > Macros > User > RewrapAndQuote
or make a key binding that will do it for you:
{
"keys": ["ctrl+enter"],
"command": "run_macro_file", "args": {"file": "res://Packages/User/RewrapAndQuote.sublime-macro"}
},
Note that since I am a purist, this wraps at 78 instead of 80 because the quote characters inserted takes up 2 characters and I am a grumpy old man; that may or may not be something you need/require. 
As defined, this selects all of the text in the view and operates on it. If that’s not desirable, you can replace the two instances of select_all
with expand_selection_to_paragraph
instead, and then the menu item or key binding will operate on the current paragraph, allowing you to use it inside of any document.