I suspect you won't even have uudecode, in which case so long as you can transfer binary files, self-extracting ZIP files should work. Might take a while for larger transfers.

Getting a Real Operating System onto the old laptop would be a benefit. You might want to look into boot-from-floppy options including TomsRootBoot and Trinux. The former fits onto a single 1.5 MB floppy ("superformatted" to about 1.7 or 1.8 MB). The latter uses 2--3 disk images to include a number of more formidable tools.

Trinux still has a Sourceforge page, though I've not dug into it. You may need to hit up Internet Archive for working images:

<https://sourceforge.net/projects/trinux/>

A 2001 white-paper: <https://www.sans.org/white-papers/327/>

Tom's Root Boot ... seems to now be offline, but has a Wikipedia article:

<https://en.wikipedia.org/wiki/Tomsrtbt>

And numerous Wayback captures. The one from 2008 should be functional and suit your hardware:

<https://web.archive.org/web/20080724163531/www.toms.net/rb>

November 2023 appears to be the most recent active capture:

<https://web.archive.org/web/20231123003805/http://www.toms.n...>

And a ~2001 article describing TRB's capabilities: <https://www.linux.com/news/little-linux-distribution-could-t...>