Hi,
Hall sensors that sense 100kHz are probably expensive, unless they improved the technology recently.
Putting a coil inside is tricky too, because it's not a spherical detector. To get the actual field readings you'd have to be able to sense the direction of the field also. Otherwise you have to assume it is oriented parallel to the coil length directly in the center. As you move toward one end, the direction will change, first slightly then more until it reaches 90 degrees from axis, then more until it points back the other way on the outside of the coil.
We could do some calculations to show the field and direction of an ideal coil, but there are probably pics on the web. Also, this will be for an ideal coil and we have no idea if your coil is near ideal or not (ideal with respect to the geometry, not with respect to the electrical characteristics). It is probably close though.
It would probably be simpler just to measure the center of the coil, along the axis, but if you move outside the coil rotate the coil in a plane parallel to say a vertical slice along the length. Rotate the coil back and forth until you get the highest reading, keeping the very center of the coil at a constant distance from the center of the large coil.
There should be no reason why you cant get relative readings this way. There wont be any base calibration to go by, but if you see a reading of 2 and then somewhere else a reading of 1, you know the field decreased probably by a factor of 2.
Inside and outside you should be able to keep the coil parallel to the big coil, as long as you dont get too close to the ends. The field should be symmetrical about a circular path around the coil diameter.