Related:
George Hockley used a Starr sabre at San Jacinto, and Sam Houston's sword is in the Museum at the battle site. The weapons used at that decisive battle are shown
HERE.
Additionally, Santa Anna's sword was captured, in the photo below. It certainly was at the Alamo. The other San Jacinto weapons would have been typical of those carried by the Texans, American and Mexican, who fought the Dictator for Independence.
The San Jacinto Battle site, Its Museum, and the nearby Battleship USS Texas (BB-35) are well worth visiting, and the traffic is probably a lot less than the Alamo. I passed by it many times while travelling between Houston & Galveston for my monthly & annual USCG Reserve duties..