Since both pours are only 8' wide and it's only 4 yards total it could be done by a DIY'r. It depends on how hard you can work and how much general diy experience you have. BTW there is more to worry about than just the appearance if you don't know what you are doing. As mentioned water is one thing, but you can also seriously affect the strength of the concrete if you don't know what you are doing.
Having said that by the time you rent the tools necessary to do it (Assuming you have nothing; a bull float, bull float handle, a hand float, an edger, and a broom) it's going to get close on cost benefit of diy. If you knew what you were doing, and again b/c it's only 8' wide, you could fashion a bull float out of wood and use a nice sturdy broom handle; ditto on the hand float. All you would really need to buy is an edger and a broom. (I used horse hair brooms, but you will want something stiffer as your job will have lots of imperfections) You still wouldn't get the best result with makeshift tools, but plenty good for what you are doing.
If you are having a hard time finding a finisher, and btw that's what you are looking for finishers - not concrete guys - call a couple concrete plants and ask to speak to the salesman. Tell him you have a project and need 4 yards for exterior concrete 3000 psi and could he recommend a crew of finishers. Tell the Billy Bob at the plant gave you their number and what would they charge to form and broom finish two pads of X square feet. You will probably be looking at a minimum fee of 500 dollars or so; so I would let the form it as well. It will cost the same either way. If it were more you could form it yourself and save some money if you had spare lumber.
Scratch the recommendation of a pump truck. A.) they are really expensive, and B.) you have a Bobcat on site; just coordinate the pour with when the tractor will be on site and load the bucket of the skid steer with concrete. Spray the bucket and surrounding areas of the machine with water (or diesel if you are really paranoid) before you load the bucket with concrete. Once you are through pouring, spray everything off thoroughly. With amount of time you will have concrete on the machine it will wash off easily. Be warned: if you don't wash it off the rental place will bring down the thunder on your wallet if you bring back a machine with cured concrete splatter all over it. You DO NOT want to wheel barrow 4 yards of concrete.
Also, the 2 inches of gravel under the shed is completely useless. It won't do anything. I would also nix the wire. 3000 psi concrete on a well prepared base (if you have any fill, or doubts about the integrity of your sub-grade, fill the Bobcat's front bucket as full as you can with dirt or rock and roll back and forth to compact the earth. If the ground moves a lot you have another issue, but otherwise that will be plenty of compaction for what you are doing.) is more than enough to handle a regular vehicle load and any load the shed will have. If you are nervous, get fiber reinforcement from the plant. At least then it is idiot proof on the install. The vast majority of wire reinforcement is improperly installed and consequently worthless. I have poured 1000's of yards of actual roads with zero reinforcement and they are just fine. Most people don't use wire unless it specified by an architect/government. If you need strength, rebar on stands is the way to go AINEC.
