Is my old screw-in fuse panel safe?

Really, to answer this question you need to have a professional inspection and evaluation of the panel. The fact is that screw-in fuse panels have not been installed in decades and have most likely outlived their expected safe service life. Most insurance companies will offer reductions in rates to replace these panels and some will not even insure a home with these outdated panels. Therefore, regardless of their condition, you should consider replacing them.