If Oswald was confident enough that the rifle couldn’t not be traced to himself, then he would not really need to hide it anyway.
And if he wore some gloves and covered his face with mask, he wouldn’t have to worry about being photographed in the SN window nor have to worry about wiping prints off the rifle.
So the suspicion of conspiracy or cover up starts with how incredibly stupid the plan seems be in the first place, which seems contradictory to the abilities of Oswald such as speaking and understanding Russian language , which indicates someone with above average intelligence.
( unless he was a Russian Oswald double)