It would be more likely that this was an ammonia or other issue other than velvet - unless you have a really good reason to suspect it (like symptoms, behavior, appearance, etc). In any case, it's simple - and I would not start over. Just leave your tank fallow (fishless) for 6-8 weeks (if you're concerned use 8 weeks). Do you have the parameters of your water?
FWIW - If you're going to add fish on 'day 1' of a cycle it's best to have already quarantined/treated those fish - then no disease can be added. There are numerous products whose instructions suggest how to properly do this. Adding fish to a tank - and then just 'seeing what happens' is not a good idea.
Depending on how long your fish were in the tank, nitrifying bacteria are probably already present in numbers such that after the fallow period is done, you can add fish. If you're concerned about this - merely add fish and a bottled bacteria product (such as fritz 9000) with which you should have no problems.