I think I would use:
i) an off the shelf hollow linear shaft as they come in various outside and inside diameters. I guess a shaft with a 3/4" ( 20mm) OD and a 3/8" (10mm) ID would work. If the shaft isn't large enough add some form of a grip. These shafts are really available off places like Aliexpress and are mostly used for linear movement. An example would be ( https://vi.aliexpress.com/item/1005008313729816.html?spm=a2g0o.productlist.main.1.7f1edY5sdY5swH&algo_pvid=da5d617e-a98c-46cd-b478-14026027a4f7&algo_exp_id=da5d617e-a98c-46cd-b478-14026027a4f7-0&pdp_npi=4%40dis!CAD!26.96!13.48!!!133.20!66.60!%402101e9a217380630172501546ef44e!12000044581316320!sea!CA!3463193163!X&curPageLogUid=rV9wvFNWFsW5&utparam-url=scene%3Asearch|query_from%3A )
ii) 3D print a shaft with comfortable outside diameter for my hand with the correct inside diameter to accommodate the stamp. Cost would be pennies to make.
Me being me I would do the 3D printed method.
kgg