Any time I add a simple syrup (2cps sugar: 1cp water) I still stir it in. If it's in a carboy then the back end of the stirring spoons or paddles are made to fit through. No need to shake anything. Side tip: if I need to stir a topped up full carboy the spoon would displace wine and overflow so I use a racking cane to stir without overflow. But What are you referring to for 4-5 weeks? A finished product? The timelines given are probably minimum time until bottling- but not drinking. The longer you wait the better it gets. Try and put a few bottles aside and taste again in 6 months. I'm thinking you will be pleasantly surprised.