No one is going to hassle you... in fact, sad to say, by human nature no one will care about you at all. People are absorbed in their own lives and arent interested in yours, so you can basically shop with impunity.
Im guessing thats not going to help you, so let me give you a more concrete answer. I have (and sometimes still do) shop in drab, and I simply act like I belong there. No one has ever said anything.
I have asked for help from sales assistants and directly told them it was for me. Many times they are actually delighted to help. Why? Because we are enthusiastic shoppers who will listen to their advice instead of ignoring them or making demands.
A few weeks ago I went into a Payless Shoes in drab and tried on several pairs of heels. Walked up and down the aisle to assure myself they fit. The store was not empty, and the only "strange" look I got was from some guy with a marine style haricut with his two kids, and he said nothing.
If you act non-threatening and just do your own thing, they wont care.
If you want to minimize human contact go on a weekday morning when the weather is bad... most times the stores are empty then. If someone says something tell them its for your girlfriend.
It will be tough in the beginning but eventually you will become indifferent to others and your fears will subside. Im not suggesting your fears arent real... I am simply asking you, are you going to stop living because of it?