You could take the Thameslink train from Gatwick to London Bridge.
Get off at London Bridge, stay on the same platform and wait for a Charing Cross-bound train (which will depart from the same platform shortly afterwards).
The train will stop at Waterloo East, the next station after London Bridge, which is a short walk from Waterloo International (the Eurostar part of the station).

Should be very painless (especially if you have luggage) and not very expensive either.