This package is named for the snan, so it is worth being plain about how the holy dip actually works - because the gap between what pilgrims expect and what happens at the ghat is where most of the trouble starts.
First, where you dip. The snan that counts is at the Sangam itself, the point out in the water where the Ganga, the Yamuna and the unseen Saraswati meet - and that point is reached only by boat. Bathing at the edge of the ghat, as many do without realising, is not the Sangam dip. The confluence is a short row out on an ordinary day; during the Magh Mela and the Kumbh it can sit several kilometres from shore.
Second, the boat. Fares at the Sangam are not fixed and the ghat is known for it - shared boats run about Rs 100 to Rs 200 per person and private family boats about Rs 500 to Rs 2,000 - and the moment you arrive, touts quote far more and begin to bargain. There is a second layer of pressure once you are on the water: boatmen and pandas pushing paid pujas, milk and coconut offerings, and donations. Experience My India pre-arranges an authorised boat at a fair, fixed rate, and our guide stays with you so no one can push a forced puja mid-river.
Third, the dip itself. You bathe from the boat, holding its rope, in moving water - the Ganga side runs shallow and quick, the Yamuna side is deep and still - so you do not wade out, and non-swimmers and elders are perfectly safe staying by the boat. Bring a change of clothes, a towel and a dry bag for your phone; there is nowhere private to change at the confluence, so people change on the boat or back at the ghat. Do the snan at first light and it is calm, cool and unhurried.
Get the point, the fare and the safety right - a boat to the true Sangam, a fixed rate, a dip taken from the boat - and the snan becomes what you came for, not a scramble on a crowded shore.