Which word should replace 'so-called' here?

Using so-called is probably OK, but when there is ambiguity about meaning (as there is in this case, with one option having negative connotations), I tend to prefer to go with something less ambiguous.

How about:

"The company sends out the documents on the designated 'Despatch Date'"

Nothing wrong with the poster, however if it needs changing, here are some words:

Are you looking for :

Nominal

As in "The company sends out the documents on the nominal "Despatch Date""

Edit: I was thrown off by the quotes around Despatch Date and thought he was being sarcastic. I did a search and found the original post and yes, I too think the use of so-called completely changes the meaning.

Do you need to use "on" or "upon" when referring to dates?

so-called is used when the following word is used in a dubious way. For example, this is from today's New York Times. ( http://www.nytimes.com/2011/05/27/us/27patriot.html?_r=1&scp=2&sq=so%20called&st=cse )

Two senators claimed on Thursday that the Justice Department had secretly interpreted the so-called Patriot Act in a twisted way, enabling domestic surveillance activities that many members of Congress do not understand.

So, yes the original post should be changed since the use of so-called clearly alters the meaning.

If there is an implication that the dispatch date may not actually be accurate, which I believe "so-called" does imply, then possible replacements include alleged, nominal, ostensible, professed, purported, supposed, hypothetical