You'll want to download it again from wherever you first got it from. A .sea file is a self-extractable file, actually an application of sorts, meaning that it has a Macintosh resource fork, like any other application. The problem with this is that PCs destroy Macintosh resource forks, making the file useless. You'll have to transfer the original .hqx file over to the Classic and decompress it on there.

The easiest way you'll be able to do it is via a floppy disk. You could make a segmented zip archive, put the segments on different floppies, and then use a Zip extractor such as ZipIt to extract it on your Classic, if you have one.

Do you have any other old Macs, perferably one with both an ethernet port and a LocalTalk port, or a external CD-ROM drive for your Classic?