If you are no longer on welfare, then you can sponsor him. No - you don't have to return the welfare payments. You must remain off welfare until his application is fully processed - otherwise the application will be refused. Expect the processing of his application to take 2+ years.
Since your husband is out of status in Canada, he does not qualify for the open work permit pilot program. This means that if you apply using the inland (within Canada) application process, your husband won't receive an open work permit until the first stage of processing has been completed. The first stage of processing is currently taking 16 months to complete. So your husband will have to wait for 16 months from the time the inland application is submitted before he will have an open work permit.
There is no way for him to get an open work permit sooner since he is out of status in Canada.