What version of Word are you using?
If this is 2003/2002 there is an option in Tools, Options, Edit tab, Show
Paste Options buttons, check this (if not already). Then when you paste the
contents of the source table, you will have displayed an icon which allows
you to choose the formatting to be applied to the content.
Beware, this will not apply Table attributes, such as borders, etc., but
only text attributes, i.e. style, font, point size, space before/after, etc.
So you will probably still have to manually format the table to the new
documents requirements.
What I have is a macro that takes plain text (created by paste special,
unformatted text) and converts it into the table (tab delimited) and applies
all the table and text formatting I require. Most of this can be done by
macro recorder. Have a play see what you get can really save a lot of time.
Also as you are working on unformatted text, you are less likely to paste
over any problem styles/table formats that could cause corruption of the
file. This is my main concern as I deal with many contributors from around
the world and their contributions can be really worrying ;-)