Links to other documents created in MS word don't work in email
Word creates links in a very odd way. The hyperlink actually looks like this:
file:///\\file path --- etc
And that format for a hyperlink will only work in MS word. What it does is tell Word that the link is to open an Office document.
There are two possible solutions
First, create the links in a text file instead of Word, and leave them as plain links rather than as text links. Alternatively, rather than a text file, you could create an email template -- just a draft email -- which can then be forwarded to whomever you like.
Second, save the document as a PDF and send that via email.