I assume by "solid handle" you mean it isn't the split handle with the wedge. If that's the case... could you just replace the handle with a regular split ended/wedge handle?
A loose handle can be temporarily tightened either in the field or in the shop by soaking the head in a bucket of linseed oil. Never soak the handle in water, except for short-term, emergency field tightening. Water will tighten the handle to the head, but the water dries out rapidly, leaving the head looser than before you started. Tightening the handle by soaking it in linseed oil is also a temporary measure. The ax must be rewedged or hung again to keep it tight.