There are 2 separate issues here, scope and hauling up the anchor the last 40' or so of anchor rode.
Regarding scope, 7:1 is really excessive if you are just going to fish. Chances are that if you are in 40' of water, you could drag quite a ways before it became an issue and since you are fishing, you will notice it. The more scope that you get, the less added benefit there is. Most anchors take something like 3:1 to set with any holding power and then have diminishing gains with scope. For example, with a completely straight rode, the difference in pulling angle on the anchor between 5:1 and 7:1 is 11 degrees and 8 degrees from horizontal. You should have more than enough rode to anchor there for a few hours of fishing.
The other issue is anchor retrieval. If you use an all rope rode, you will just have to retrieve the water weight of your anchor which is around 40lbs. However, if you have a lot of chain, the weight will become much greater. The advantage to shallow water and chain is that you never have to pick it all up at once. Depending on how your boat is laid out, you may well be able to use one of the halyard winches on the mast to haul up the anchor although this can be difficult if you are using chain. With a little bit of work on the helmsman's part, you shouldn't have to do anything until the anchor is broken out.
As long as you are reasonably fit, this is completely doable.