My first piece of advice is that you should get used to the idea that some branches sole purpose is to hold foliage that make the trunk thicker or just help the tree from getting bigger. Once that purpose has been accomplished you should simply discard it - it is of no use any longer.
There are, however, many circumstances in which the plant will not produce a new branch where you might want one to be. Grafting is the only way that you will ever get what you want, so you should give it a try (several times, actually - grafting success is mostly a matter of practice).
What you seem to have in mind is a side graft. You would make an angling cut in the stem into which you will fit the branch you pruned (the scion). The challenges are that you much make the cambiums of both parts align and you must provide a humidity enclosure specifically around the scion's foliage so that it will not desiccate. For the graft to take, the cambiums must grow to produce a connected xylem (wood) that will supply water and minerals to the scion from the stock's (mother tree's) roots. This can take months to occur. Most frequently, a small plastic bag with a bit of damp sphagnum is closed around the scion stem, enclosing all the scion's foliage. Another way that can be used with conifers is to wrap the foliage in parafilm.
The alternative method is approach or thread grafting. These methods have the advantage that the scion is either a long branch still attached to your ficus or is another young seedling that has its own roots. With thread grafting the thin stem (whether be an existing branch tip or a seedling stem) is threaded through a hole drilled in the trunk, just like threading a needle. This can only be done with a bare stem that can subsequently grow new leaves. In your case, you would carefully cut off the leaves, being careful not to damage the axillary bud at the base of each leaf petiole. Once threaded through the hole, the scion must be stabilized so it doesn't move which can be done by wedging tooth picks in the hole under the scion. Once the graft has taken, the scion is cut loose on the entry side.
Approach grafting is similarly done, but instead one cuts a slot across the stock's stem into which the branch/stem is snugly fit and then secured with a zip tie, padded wire, or thumbtacks/nails. Again, as the scion grows it fuses with the stock which take months, and maybe more than one growing season, to happen. The reason for the ties/nails is that the growth of the scion cambium also tends to push the scion out of the groove. First carefully cutting away the bark and cambium, exposing the wood, on the side of the stem against the stock will ameliorate this, but may also accidentally kill the scion.
Lastly, you could just try to root the branches you remove. In addition to just giving you more plants to work with, you can use rooted cuttings as scions for thread or approach grafts - you just need to secure the pot to the stock tree until the graft has taken. This way might be more rewarding as you will still have your live rooted cutting even if you've used it trying to make grafts that failed.