VIM: find all numbers in double quotes and remove double quotes

I've accidentally formatted a huge file incorrectly. I have several hundred vars defined as:

"exportOrder": "274"

When I really need:

"exportOrder": 274

Anyone know a regex to remove the double quotes in each of these occurrences?

The sample data looks like so:

{
    "key": "date",
    "name": "Date",
    "datatype": "date",
    "exportOrder": "274"
},
{
    "key": "coordinates",
    "name": "Coordinates",
    "datatype": "geoPoint",
    "exportOrder": "275"
},

and so on..

I can remove the first quote with: :%s/Order": "/Order": /g

but can't figure out the 2nd quote.

Thanks