Depending on where you live, this might sound controversial, but children don't need protection from their parents as long as they don't engage in violent, sexual or otherwise unhealthy behavior in front of / with the children.
Painting your nails, dying your hair or even dressing in feminine clothes is not sexual or unhealthy behavior, it's you living your gender identity. Other parents may grow a beard after being clean shaven for years, start listening to hard rock music or decide to become vegan. Where's the difference from the perspective of a child? There is none.
Many families nowadays get divorced (or break up if they weren't married) and the children have to get used to having a new mommy or a new daddy. Are they traumatized by such drastic changes? I'd argue the biggest risk of traumatizing is the arguments and fights of the parents, not the introduction of new partners. You living your gender identity more openly is certainly less traumatizing than a divorce.
Where I live, same gender families are becomming more and more publicly acknowledged and accepted. Same gender families can also marry and adopt children. Those children grow up with the knowledge that they have two mommies or daddies or even that mommy was a boy when she was a child. It's what they are used to and just the natural state of their family. They aren't traumatized when learning that the vast majority of children have one mommy and one daddy instead of two.
The daughter of my friend grew up with the knowledge that she had two uncles instead of an uncle and an aunt. She went to an evangelic school and openly opposed her teacher who wanted to convince her that only an aunt and an uncle could be a "family", because she witnessed the love between her uncles and all other family members confirmed that her two uncles were a family. It was her natural state of the family and no teacher could change that.
Another daughter has a teacher who physically and legally transitioned during summer break. This wasn't a surprise to any teacher or student at the school because the teacher already adapted gestures, mannerisms and a clothing style that could only be considered feminine. She didn't even change schools or classes after her transition. Granted, there were some obstacles (as there always are), but the students accepted her new identity much easier than the fellow teachers.
On the other hand, I've heard of homosexual men who lived a heterosexual live and had children for decades before finding the courage to come out and seek the love of another man. Some of those stories have a sad end, because the (now adult) children grew up expecting their dad to be "normal" and couldn't accept the seemingly new identity of him.
The reoccuring theme here is: The younger a child is, the less traumatized it's going to be by your change and the more accepting it will be. The longer you hide your true identity behind a mask, the more "normal" this mask will become. When you finally decide to drop the mask, your child has to get used to a new "normal". The sooner you drop the mask, the sooner will your child accept the true you as normal.
The way your question is phrased suggest that your wife is not afraid of traumatizing your doughter, but of people gossiping about you and by proxy her. It sounds like she uses your daughter as an argument to force you to keep your gender identity secret. She (rightfully) is afraid that if your daughter witnesses your trying things out, she will speak about it with other people. The things to realize here are:
- Of course she'll speak about it. Why shouldn't she? For her there's no reason to keep your behavior a secret. At 4 years of age she doesn't have such a strict black-and-white understanding of gender and doesn't see a reason why she shouldn't talk about you painting your nails.
- It's the other adults that have a black-and-white concept of gender and will certainly be less accepting. It's the adults your wife is afraid of, not traumatizing your daughter.
Unfortunately, resolving this conflict with your wife is not on topic here. If problems arise, Interpersonal Skills SE might be the right place to ask for help.
To aid you in your search for scientific studies concerning children of transgender parents, I invite you to read:
Compared with children referred to the same clinical service regarding concerns about their own gender identity, the children of transsexual parents were less depressed and less likely to report peer harassment, persecution or victimization. However, the case notes of children of transsexual parents revealed that this group was more likely to have experienced marital conflict between their parents than were children referred with gender identity concerns and as likely to record difficulties in parent-child relationships and general difficulties with peer relationships.
A good starting point for further research is Google Scholar.