How do I approach this question?

In 1861 and 1862 Little Rock was the main assembly point for Military stores for the Army of the West and The Army of the Southwest the next closes arsenal was at Fort Smith. The Army of the Southwest that Van Dorn commanded was as well equiped as it could have been in March of 1862 at the Battle of Pea Ridge, yet some of Van Dorn's men were poorly equiped and some without arms all together, from some accounts. So there couldn't have been that many extra arms setting around in the arsenals that weren't being used to start with.

Hindman as he was reorganizing was using anything that he could get his hands on. He recieved small shipments of arms including some enfield rifles from various sources but only in small quanities maybe a 60 or 70 in all. He ordered all guns in private hands to be purchased for the army. One brigade under Col R.G. Shavers in July of '62 at Pine Bluff was issued 16 doublebarrel shotguns and 2000 rounds of ammunitions for the entire brigade.

Hindman ordered that at the Little Rock U.S.Arsenal that the discarded unserviceable artillery barrels that had been decommissioned prior to the outbreak of the War and had been buried as corner border markers of the Arsenal property to be dug up and refitted for service. He also ordered every commissary officers to seize any store of cartridge papers in Arkansas and send them to little Rock and any gunsmith to come to Little Rock with their tools to be placed in service to repair the broken guns that were not taken by Van Dorn.

Fortunately for Hindman most of the early Texas regiments which Governor Rector stopped in Arkansas that were headed east had their own weapons with them. Particularly the 12th and 21st Texas Cavalrys. the 6th and 10th Texas Infantry and the the 24th and 25th Texas Cavalry which was dismounted after arrival in July Most of the Arkansas Cavalry companies that Hindman used such as Chrisman's had equiped themselves from home.

When Gen M.M. Parson's Brigade returned to Arkansas from Van Dorn's Army in Mississippi, he brought with him a wagon Train of quartermaster supplies and 25 pieces of unattached artillery and supplies August of 1862. At the same time a shipment of 11,000 arms arrived at Pine Bluff from Vicksburg by way of Monroe, La. out of a shipment of 18,000 that were originally sent. 5,000 of those 18,000 were captured on the steamer "Fair Play" by the Union and 2,500 of them went to Genrl Richard Taylor army in Louisiana. These weapons had come from the arsenal of the entire Confederate States that had been returned to State arsenal as the Confederates had reequiped themselves with the better captured Union arms. It is reported in the OR's reports of the "Fair Play" that some of those weapons had come from captured Union weapons at the Battle of 2nd Manassas. There was a Confederate War Department Investigation over the Capture of the "Fair Play"

There are other reports such as Albert Pikes complains about his command being stripped of arms to equipe Hindman troops. and the argument over his not sending weapons with Dawson's 19th Arkansas, when it was returned to Little Rock, and the lost of Woodruff's Battery that all point to the situation as being that Hindman was almost totally destitute of military quality weapons. And could hardly arm or issue ammunition to the few troops that he had in June of 1862. And that until the shipments of arms in August of 1862, Hindman struggled to arm his conscripts. Even at that Walker's Teaxs Division was still using Mexican War Flintlocks and conversion Muskets during it's Louisiana Expedition in 1863.

So there is little evidence that Van Dorn left very much in Little Rock at least that could be used to defend the state.