Officers in the RTR carry Ash Plants as part of their SD. This started in WW1 when Officers would walk in front of the tanks as they advanced using a long ash pole to test the firmness or otherwise of the ground. Needless to say their life expectancy wasn't particularly high.
Right listen up class here is the story of the swager stick.
The swagger stick was also originally used as a measuring device. It was split down the middle with the bulbous end (sorry to easy to make jokes about it so I won't bother) acting as the pivot, a bit like a school compass but obviuosly a lot bigger. It was spun in the hand as the user walked, so that it measured out paces. It was used in drill training so that the infantry all walked at the same pace and stride, as we all know most of them find this difficult to do, as they have to breath at the same time. It allowed them to get mown down as cannon fodder in nice neat rows. As it slowly fell out of fashion it was gotten rid of by most regiments and ranks. However as it was a show of rank (only RSM's and officers were allowed to carry them) some kept it, but in a nice stick form that can no longer spread it's legs (sorry again, too easy).
Right history lesson over.
Thoseof us in Dark Blue still see them occasionally with the Commander (that's 2 1/c to you brown jobs) of a Barracks or big training establishment. They normally come accompanied by a black labrador, for some reason!
Think you may be confusing the pace stick with a swagger stick.
As far as I know swagger sticks are (were) carried by the infantry gunners and the signals. The Cav carry riding crops, and the above RTR and Irish variations still stand.
Problem is Barrack dress has pretty much disappeared, as CS 95 is the order of the day.