If yes, what would that cost? What factors affect the cost?
Older fuse panels can be dangerous along with the possible older wiring that usually accompanies them. If you are questioning the safety of the panel, it would be best to get the advice of a licensed, reputable electrical contractor. As far as the cost goes, it could be anywhere from a few hundred dollars to a few thousand dollars if the job requires rewiring or drywall work to complete the new panel installation.
We would recommend that you do. The cost may not be as much as you expect and the peace of mind is, of course, priceless! If you are planning to do any home remolding and permits are being pulled, some states (TN does) will require you have the box brought up to current code standards.