There really isn’t any correlation between carrying a hound whip and carrying a bat. (I am of the carry a bat on everything, always, school of thought.). One is used to signal or correct a hound, the other is used to signal or correct a horse. Using a hound whip in place of a bat is clumsy and ineffective for the most part.
I am still firmly of the opinion that if you are not familiar with hounds, haven’t been walking out or roading hounds, aren’t likely to be drafted to help staff, you really don’t have any business carrying a hound whip. (Note: it’s not a hunting whip, it’s a hound whip)
If you want the handy gate handle/horse catcher/glove retriever, take the thong and lash off and ride with just the crop piece - still not terribly useful as a crop, but handy for gates. It used to be common practice for people to remove thong and lash for the summer and ride out with just the crop end while legging up.
Yes, at checks or casts while hunting, I have been in tight places in the woods while errant hounds ran through the field to rejoin the pack, and in those situations, if I had a hound whip, I would have let the lash down to keep the hounds out from under my horse. However, hunting horses need to learn to accept hounds underfoot, period, full stop, the end.
If I was a huntsman or a master I can’t imagine anything more frightening than hunting in trappy country with a large field all equipped with hound whips!