Regrettably hammering a drill chuck onto its taper will almost certainly wreck the tapers.
Right way to do the job is to sit the chuck on the taper adapter wit the tang side down and bang the tang end down hard on a solid, non deforming, surface a couple or three times. The jolt and vibration should set the taper so tight that its immobile without wedges or an extractor. If it doesn't one or both tapers is bad enough that, short of welding, the thing will never hold.
Are you sure the tapers actually match.
Some of the metric B series are so close to the JT series that its nigh on impossible to tell the difference without careful measurement. Except they won't hold. B16 I believe is the example I ran into long enough ago to have forgotten the details.
If the chuck is an inexpensive one, most likely of a certain vintage, it may not have a correct to spec taper in the body. The aforementioned B16(?) issue was with a chuck that could not be re-attached to the arbor it came with. Investigation showed the chuck body taper to be pretty much midway between the B series and the closest Jacobs. The arbor was to spec and had clearly been pressed on with very heavy force. I ended up re-cutting the taper in the chuck body to correct specification and cleaning up the scrapes on the arbor. Chuck body was quite soft.
Clive