If you had successfully decoded the BinHex (.hqx) and decompressed the StuffIt (.sit) using a later version than StuffIt Expander 5.5, that ought to be OK, in principle. However, if this was done on a Mac OS X machine, something could still have happened to the file before or during transfer to the iMac G3. If, somehow, the decoding and decompression was carried out on a PC, there would most certainly be a resource fork loss/problem.
Did you see the special Burn program icon (not only a generic icon of some kind)?
Anyway, if a USB flash drive or a CD-R is used for the transfer from the current machine (be it Mac or PC), keep a downloaded .hqx or .bin file exactly as it is until it arrives on the iMac G3. As indicated above, carry out all decoding and decompression operations on the destination computer.
Alternatively, you could connect the Ethernet port on the iMac G3 to one of the LAN ports of a router, and thus access the Internet directly. Even an existing very old browser version may be sufficient for old Mac software downloads from some freeware/shareware archives.