KathyLauren makes a key point.
The key to all this is to finally develop the frame of mind that what you are doing is unremarkable, entirely normal, nothing out of the ordinary. If you shop with this sensibility about you, salespeople and other customers will treat you, for the most part, like a welcome customer and do so with respect and dignity. If you go into the store with the demeanor of a criminal on the lam, you will attract unwanted attention and appear as though you are actually out of place or even potentially an odd ball or up to no good.
The big box stores are low stress as nobody is really paying attention or really cares as long as you are not stealing, harassing other customers or planning an antisocial act such as arson. Don't try to pull off one of the typical facade acts such as "I am buying this for my wife" or the shopping list strategy, "I'm looking for this mascara [brand and type/color written on the written on the list], can you help me?" The stress signals will be evident in your behavior and voice, you will look like a fool, you will not get away with it. If, on the other hand, you muster the courage and go into the encounter as yourself buying for yourself, paradoxically your stress levels will be much lower since you are not presenting a deception hoping to have it be believable, which it will almost certainly will not be.
As has been said many times, nearly every store and employed salesperson in the current mainstream retail world exists to serve customers and sell merchandise for the purpose of remaining in business and generating revenue and ultimately profit. Salespeople want to make... sales, not harass you. Save for a rare loony fringe individual that slipped past the HR sanity scrutiny, an employee who will be promptly fired if creates a hostile atmosphere for you or insults you, you have nothing to fear from the sales staff.
I recently went into a major upscale mall department store to buy a short satin chemise nightgown. Size XXL for me dressed in guy mode. I was in the store on a weekday at the end of the workday on my way home and the store was pretty busy with lots of shoppers. I strode directly into the women's department to the intimates section and shopped. This was a first for me and I had a slight bit of anxiety about it but was overall pretty comfortable with the idea. There were several cis women in the immediate area where I was shopping. Occasional pleasant smiles of acknowledgment were exchanged but no piercing looks or creepy feeling from them. I shopped for about a half an hour, took my 2 selections to the register to pay, the entire transaction really pleasant and fun.
If you know all your sizes, there are a multitude of opportunities to shop online and in the world's biggest marketplace, Ebay. With these, there is no need to overcome fear, just turn on you computer and shop with credit card or PayPal account ready to go.
Still, shopping in physical bricks and mortar stores is fun and the sales people are generally pleasant. The biggest issue for many of us is the "outing" risk. Having not come out to my wife, family or friends yet I would have been mortified to run to my next door neighbor in the intimates section at the department store buying a XXL nightgown when she would clearly know it could not have been for my wife who is a size small. The speculation would start with the incorrect and most damning assumption that it was for another XXL woman, not me. This would not be how I would like to disclose my life's biggest and only secret. The world is a pretty small place depending on your work place, social circle and where you live you might be surprised to find that you were not a stealthy as you might have thought.