Good evening, I'm Dr. Sara. I'm a licensed veterinarian who works exclusively with dogs and cats. I'm sorry to hear that your pup has sustained this injury.
Do you think there'd be any way you could get some photos to attach? That would be quite helpful, I think.
If not, that's OK. You've described it well enough for me to have a general idea of what you're seeing. As long as no subcutaneous fat or muscle tissue is poking out of the laceration, you are right in your assessment that it's likely to heal on its own. Really all that's needed is gentle wound care to keep the area clean. In some cases where there's a piece of skin hanging off at an angle, the skin flap that's hanging will become devitalized, black, firm, and fall off. If I can tell a skin piece is going to be nonviable, I'll often cut it off when I'm debriding the wound. I wouldn't necessarily suggest that at this point, though, as usually when I'm debriding a wound I've got either general anesthesia or at least ample local anesthesia. The location being a high motion area can cause a frustrating experience with healing in that each time the skin pulls, it may pull open the skin edges. At this point you're not going to get primary healing with those edges, so there's no need to keep apposing them. The glue may have helped initially, but now there's no need to continue to try to keep the skin edges together because they're no longer going to heal directly to each other unless some surgical debridement is done to freshen them up. In cases where primary closure isn't going to happen, we wait for what we call second intention healing, which is where skin cells migrate across the defect slowly to fill it in. Often this happens either on a healthy moist granulation bed or under a scab. So my advice with smaller wounds that aren't going to heal primarily is to allow a scab to form and let the "old guys" do the work. By "old guys", I'm referring to "Mother Nature" and "Father Time" :)
With larger wounds, you may need to keep the granulation bed moist and healthy. One way to do this at home would be to apply a small amount of honey each day, rinsing yesterday's off if any still remains before applying new. If a scab is forming, though, this is mother nature's "band-aid" and I allow it to stay for as long as necessary.
If you're able to attach pictures I'd be happy to review them and adjust my answer accordingly.
Best of luck - please let me know if you have other questions!