Since my this particular question didn't get any answer, I thought of asking a more focused question, along a path which seems a bit more feasible after few tests.
Is it possible to install the antenna of the 433MHz ASK/OOK TX module, some distance away from the module itself ? All my present tests use the antenna wire directly attached to the module, and of course, they work fine. However, if I add a length of wire to increase the distance of antenna, the whole wire, I believe, would behave like an antenna - right ? And that would detune the antenna ? Any solutions to the problem where TX module and antenna need to be spaced out ?
Based on the comment (PeterJ's) and answer (pjc50's) so far, here's what I understood as the possible solution.