/usr/share/dict/words isn’t normally modifiable by non-root users, so your regular use of programs using it for spell checking wouldn’t modify it.
In fact, since it’s in /usr, on most systems it “belongs” to the system and is only modified through updates to the system (in your case, Ubuntu). At least on Linux systems it’s usually one of the word lists provided by SCOWL (Spell Checker Oriented Word Lists).
As such, it’s safe to copy and distribute, as long as you follow the license terms. Another approach might just be to rely on /usr/share/dict/words on your project’s users’ systems — you mention you don’t want to do this, but in many cases the file will be the same as that available on your system. This can even include CI — on typical Ubuntu-based CI environments, install wamerican to get the default US /usr/share/dict/words file.