The episode in question was called Man Hunt, first shown in the third series on 27 November 1969. Like all but a few Dad's Army episodes, it still exists and turns up in the series' not infrequent repeat runs. In fact it was Walker, not Jones, who had turned the parachute into knickers. Well, it would be, wouldn't it? Incidentally, in the final scene it was Mrs Pike whose knickers were exposed. So, not much to get excited about there.
I was intrigued by your description, as, though I have seen the episode several times, I hadn't identified this as even an off-screen spanking. So I got the tape out to see (or hear) for myself. The action is more or less as you describe, but while there are female yells on the soundtrack, what precedes them sounds more like thumps and crashes than slaps: to my ears the implication is that he is beating up his wife rather than spanking her.
One good thing is that the scripts have just been published for the first four series of Dad's Army, so it should be easy enough to check the stage directions to establish what the original intention was.