Tamara,
I wonder whether this will do the deed, always keep a backup of original artwork to fall back on:
1) Select everything, then in the Object dropdown click Path then click Offset Path and insert a (positive) value large enough to make the paths overlap;
2) In the Pathfinder palette apply Unite/Add to shape area (top left, the one that shoew the shape becoming one);
3) Repeat the Offset Path from 1) with the same value, only negative.
This ought to give you a path following the outer bounds of the artwork, closing gaps if needed.
You can try with different values of Offset in 1).