"If anyone knows of a shell which meets my criteria of being lightweight but with command history and tab completion (paths, command names and command arguments), I'd really appreciate any suggestions. Otherwise I may have to look into extending dash or something."

I would also love to know the answer to this question. I am a big fan of shells and shell programming in general and POSIX shell in particular.

Only suggestion I currently have is ksh, of which there are a few implementations, ksh93 still developed (https://github.com/att/ast), pdksh from OpenBSD (of which there is a portable version here: https://github.com/ibara/oksh) and MirBSD ksh (https://www.mirbsd.org/mksh.htm).

Otherwise of interest is mrsh: https://github.com/emersion/mrsh which was recently mentioned by Drew DeVault in a blog post linked here: https://news.ycombinator.com/item?id=18777909.

EDIT: And by mentioning mrsh, I meant it as a better/easier base to extend to get what you are asking for.