Overall the best way would be to power the HDD from a hub with your "Y" cable and then plug your USB A to micro B into another hub port. That is the simplest way to do it, reduce the cable mess and use only one PSU. This involves no cable cutting, wiring or soldering. Buy the shortest cables you can find and you will have an easy to use setup.
I would definitely check that that adapter does not back-power the RasPi or add an inline fuse and just back-power. That would probably work just fine with a 2A PSU. If you try that cable please report if it works with or without back-powering the RasPi. There are many people that are trying to run HDD with as little investment as possible. I am sure they would be interested.
I am assuming that you are not looking to back-power your RasPi, but here are some other ways.
I have back-powered RasPi with a USB to SATA with "Y" adapter. By plugging the Data/power cable into the RasPi, then plugging the power only cable into an iPad2 charger (back-powered). This does work but there is no over-voltage protection. I have also used an A male to A female with an Adafruit adapter to the lower USB and the HDD in the upper. A Seagate drive (single short USB cable) fired right up with that setup (back-powered). So there are a number of ways to do it, but look for the safest way when possible. Sometimes I just do not follow my own advice
If you go to my web site you can read about that setup and about back-powering in general if you are interested.