Well at least you didn't start messing with the head gasket, that could've been painful! 
Unless you are fortunate enough to have one of the few Yamaha dealers left near you, and by a million to one chance they have your part in stock then i doubt very much you'll get your hose today! Alternatively if you have a bike breakers nearby they may have one if you're very lucky!
I can't tell by the photo whereabouts that hose is but try this site: http://www.yamahascooterspares.co.uk/spares/epc2.asp?modelID=9655&PageiD=7&m=YAMAHA+FZS600+Fazer+RADIATOR%2E+HOSE&uID=0
Or maybe this one: http://www.yamahascooterspares.co.uk/spa...ETOR&uID=0
If it's not there, go back to the main page and enter your bike again and look through the menu.
I just thought, if it leads to the carbs it might be the pipe for the carb heater circuit. There are some small hoses that go around the carbs to try and keep them a little warmer in winter to avoid carb icing. They get blocked with crap very easily because they are so narrow though.
Also, when you've sorted the pipe, do what i said earlier and leave Rad Flush in for 2 or 3 days of riding. If you have a clogged up system it works so much better over a few days rather than the suggested 10 minutes ticking over or 10/20 mile ride, or whatever it says on the bottle. It will heat up and circulate when riding, but then just sit and soak overnight, then when you ride again the next day and circulate the fluid any crap will break down much easier. But be sure to flush the system with a hosepipe when you're done to get rid of any loosened debris.
Unless you are fortunate enough to have one of the few Yamaha dealers left near you, and by a million to one chance they have your part in stock then i doubt very much you'll get your hose today! Alternatively if you have a bike breakers nearby they may have one if you're very lucky!
I can't tell by the photo whereabouts that hose is but try this site: http://www.yamahascooterspares.co.uk/spares/epc2.asp?modelID=9655&PageiD=7&m=YAMAHA+FZS600+Fazer+RADIATOR%2E+HOSE&uID=0
Or maybe this one: http://www.yamahascooterspares.co.uk/spa...ETOR&uID=0
If it's not there, go back to the main page and enter your bike again and look through the menu.
I just thought, if it leads to the carbs it might be the pipe for the carb heater circuit. There are some small hoses that go around the carbs to try and keep them a little warmer in winter to avoid carb icing. They get blocked with crap very easily because they are so narrow though.
Also, when you've sorted the pipe, do what i said earlier and leave Rad Flush in for 2 or 3 days of riding. If you have a clogged up system it works so much better over a few days rather than the suggested 10 minutes ticking over or 10/20 mile ride, or whatever it says on the bottle. It will heat up and circulate when riding, but then just sit and soak overnight, then when you ride again the next day and circulate the fluid any crap will break down much easier. But be sure to flush the system with a hosepipe when you're done to get rid of any loosened debris.
More people are born because of alcohol than will ever die from it.