I don't know that this method is any "quicker," but if you want to use key-strokes rather than mouse-clicks:
1. While in city view, hit "c" (for change), this will pull up the table of different units/improvements/wonders you can build in that city.
2. Hit the key for the first letter of the unit with the right number of shields you wish to buy: "w" for warrier, "h" or "p" for horseman or phalanx, respectively, etc. Hit return. This will change your production to that unit. (If more than one production item begins with that letter, you may have to hit it multiple times, as the program will scroll through the available options.)
3. Hit "b" for buy.
4. Repeat this process for the next layer of shields you wish to irb.
It's still a pain, but I prefer it to mouse-click.
Note: you cannot do this while viewing a city during the pre-turn production phase (at least, you can't without also having to use mouse-clicks). Just wait until the actual start of your turn and then get into the city view, as above.