You certainly can install a ball joint with a ball peen hammer but it is not recommended. It is very important that the joint is pressed into the control arm with even pressure all around. If even pressure is not applied it could warp or shave away areas on the upper control arm. Although this is a tight fit now, in a year to come it may be able to slide right out if water, rust, etc is able to form around there.
I don't mean to be a nag but too many people make mistakes on vital suspension parts like these. I nag for everyone's safety. (This pops out while at speed, well, you know what would happen) I'm having the same issue with my explorer, the boots are torn and it's time to replace. My UCA's are both rusted, deteriorated, and all the bushings on them are old and rotted. To me it's much more economical to replace the entire UCA assembly in one go. This way there's no pressing, no guessing. If you don't have the proper tools to press ball joints I would recommend this route.
I got two UCA assemblies from MOOG for $230. These both have joints with grease fittings and come with everything necessary to replace the factory parts, bushings, joints, and bolts. The old one's are simply unbolted, and new ones put in the same.
In the end, if you feel confident with it, go ahead. If there's any doubt, reconsider and invest in the proper tools or the entire assembly for the future.. and YES, you should replace both ball joints/UCA assemblies at the same time. The reasoning behind this is not because we all have OCD, it's because if the ball joint you showed us here popped out, how long until the other side pops as well? Not worth the risk.. Always replace in pairs, you'll thank yourself later.
