Those are the boxes I was thinking of.
Paragraph two of the ACBL Bidding Box regulation, regarding the stop card, says
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Place the stop card so that LHO sees it (the skip bidder is responsible for gaining LHO's attention). The skip bid is made. The stop card is replaced in the bidding box.
If you place the stop card face down next to your bidding box after using it, I hardly think an opponent (or anyone else) could claim you've used the stop card for every bid. Granted, it's a deviation from the correct procedure specified in the regulation, but I don't see it becoming a problem.
The ACBL Codification (see the web site) says
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For sanctioned games at clubs, the club may elect to discourage it's [sic; the stop card] use and require no mandated pause.
Given that the LHO of a skp bidder routinely ignores the use (or non-use) of the stop card, and that TDs rarely, if ever, do anything about breaks in tempo after a skip bid, I do not see how the regulation's stated goal of protecting the rights of both sides is met. Therefore, I favor not using it at all.