Deleting the skeleton causes the model to disappear (by the way, the model's size and position also depend on the skeleton), but leaving the skeleton in place causes the editor to complain about more than two skeletons in the model during export...
I've tried different methods, but there's a fairly simple way (but my knowledge is limited to 3Ds Max, which is why I found a way to avoid using Maya):
1) Load the model with the skeleton, make the necessary changes to the size and position of the main bone of the skeleton (as a result, changes will occur to the model itself, which is attached to the skeleton).
2) Export the model with the skeleton to SMD. If the model has one material, it will be merged into a single mesh during export; if there are several materials, there will be several independent meshes with different materials (and the "Multi\Sub-Object" property will be added to all materials, which can then be removed if necessary).
3) Delete the model, leaving only the skeleton, go to the "Bone Tools" bone settings, select all the bones of the skeleton, and click the "Reset Stretch" button. Save the skeleton separately (you can save it in the 3D Max format).
4) After that, you can load the separately saved skeleton and then import the previously saved SMD file with the model on top of it (and you will get a model and a skeleton of the same size and orientation in space).
Unfortunately, I don't have 3ds Max, and I don't want to buy it either.
I suspect the problem is an incorrect conversion from SMD to FBX.
К. Прутков-инженер. Мысль № 77.
Многие вещи нам непонятны не потому, что наши понятия слабы; но потому, что сии вещи не входят в круг наших понятий.
© Козьма Прутков