Some people have stated that they have used low dose hormones for the very purpose you described. Results vary from person to person.
We do not discuss exact doses, but in general if you take the normal transition dose and reduce it by 80 or 90 percent, that would qualify as low dose.
Feminization is not dose dependent. Some ladies have taken transition doses for years and have little to show for it. For most people, a low dose will still feminize but it may take longer. The goal of any dosing regimen is to mimic the hormone blood levels of natural born women. Staying below those blood levels may or may not do what you want. If the regimen your doctor prescribes does not feminize, it also may not relieve your dysphoria.
As for negative side effects, many of us here recommend a non oral estrogen. Either topical, injectable or sublingual to minimize side effects. studies have shown these to be quite safe at most all doses currently prescribed.
