While you know how to assign new shortcuts for opening the app I have a solution to open new "Chrome" window if it is not present on current Space or activate the "Chrome" on current space.
This AppleScript will prevent you from switching the spaces:
if application "Google Chrome" is running then
tell application "System Events" to set CurrentSpaceWindows to windows of process "Google Chrome"
if CurrentSpaceWindows is {} then
tell application "Google Chrome"
make new window
activate
end tell
else
tell application "Google Chrome" to activate
end if
else
tell application "Google Chrome" to activate
end if
You can now assign a global shortcut to run this script and get what you want (If I understood you correctly).
I personally prefer to use BetterTouchTool to assign keyboard and other shortcuts. You can directly assign a shotcut to run this script.

EDIT: add a posibility to run it from an Automator.
In order to run it via Automator Service, you have to create it like so:

Please note, that I've left the whole part:
on run {input, parameters}
<- Here goes the Script
return input
end run
Later go to System Preferences -> Security & Privacy and add Automator to the Accessibility section like this:

Then it should work as expected, I've tested it and it works.