Chalking the hands will dry them out and can damage the skin over time. If attention is not paid to recovery, this damage will accumulate and increase the risk of skin tears. A similar impact on performance can be achieved by using rubbing alcohol to clean both the hand and lifting implement of any sweat or oil prior to each attempt at a lift.
Chalk can be purchased in most sporting goods or outdoors stores. A 1lb box of 8 blocks will last a long time and should be under $10. Be sure to get gymnastic chalk (Magnesium Carbonate) and not pool chalk or playground chalk. Some gyms have a policy against allowing the use of chalk. A resin ball, a chalk ball, or spray on chalk can be tried in those locations as discrete alternatives.
File down large or rough calluses to prevent them from ripping off while training (use a pumice stone or gripper handle). Moisturize the hands to prevent dry skin that flakes or splits. Minimize use of chalk and improve environmental factors like low humidity or chemical exposure if dry skin tears become a serious problem. Damage on friction based lifts can be minimized by using a thin cloth between the training impliment and the hand.
Skin tears are unavoidable when training the grip, but care should be taken to minimize them. When a tear occurs, it usually smart to rest until the skin heals. If resting is not an option, there are ways to continue training. A little chalk in the tear may be enough to finish the session. Another option is to cover it with athletic tape. Some lifters will close the skin with super glue. If lost skin is a regular occurrence, there is a problem with the training program.
The larger balls can get quite heavy and are used to stretch and strengthen the hand in the most open positions. People looking to train this way often use javelin training weights or (for the heaviest work) small shot puts in place of the baoding balls. Some will even wrap the heavy balls in duct tape to add friction and make work with them even harder.
Palm facing up (supinated)
With a little persistance, a person having 7" hands can expect to work up to 4lb shot puts for the first four exercises. The last two are primarly ways to show off and have limited practical application for someone focused on grip strength. Once mastery has been achieved with a specific size of dexterity balls, the hand can be flipped over for a more intense challenge.
Palm facing down (pronated):
While at first these exercises may seem impossible, a person with 7" hands is capable of building up to 2" or even 2.25" balls with the hand facing down. This is a great way to develop independent control of the fingers while investing in hand health.
Avoid stress balls made of foam, gel, or filled with sand. They are not durable and will tear or split.