Should the Chandrakhani trek be done without a guide? If yes, what preparations should be done and what should the itinerary be like for a person starting from Chandigarh?

It is always advisable to hire a guide, as they know the place very well. This pass is easy to moderate hence you can prepare your body with minimal exercise and stretching. You can begin your trek from Kullu in Himachal Pradesh. If you are from Chandigarh, take a Volvo from any major bus station and get off at Kullu. If you want to take a flight, then arrive at Bhuntar airport and take a local bus or taxi. The nearest available railway stations in Pathankot and Jogindernagar.
You also need to get yourself the necessary gear for your trek. This includes a backpack with rain cover, waterproof trekking shoes, warm and waterproof jacket, trekking pole, head torch, etc. If you want to save some money then rent these gears instead of purchasing them all. This is a better choice if you are not going on treks regularly.