In practice, however, the concept of a retarding parachute went away very early in the employment of either a single launcher or a Y launcher . . . see
and was not used, at least by the USN, in WWII. The ballistics of a launcher were pretty straight forward and could by slightly modified by selection of charge size used in the launcher.
Further, a depth charge fired from a launcher presents little hazard to the ship as the charge is “thrown,” as they say, off to the side of the vessel to create a larger danger area, or pattern, for the submarine as is shown in the first reference above. This pattern is to take into account possible attempts to maneuver by the submarine. But if you are using, solely, a launcher, be it one or two barrels, the speed of the vessel is relatively immaterial in terms of potential damage from your own charges. Where speed becomes important using launchers is if you have more than one, the speed of the ship, too fast, can lessen the density of your pattern relative to your rate of fire.
A charge rolled off the stern could certainly present a problem if one’s speed is insufficient to clear the blast area. That is a calculation one has to make . . . for what depth is the charge set . . . on average, how long for the depth charge to reach that depth . . . how fast should the ship be going so as to be, oh, say, 3 times the blast radius, or about a minimum of 75 yards from the point of the explosion. So, if the depth charge drops off the stern and takes 10 seconds to reach its discharge depth - not very deep if the sink rate was about 8 feet per second as was typical for the US Mk II type - it might be a good idea to be pushing about 13 knots, 14 would be better. Not all that hard to figure out once you know the depth charge sink rate, the effective blast radius and how much of a risk you're willing to take. Your results may vary.