I can't provide any specific recommendations for any businesses, but I can tell you that there are companies working with nuisance wildlife that specialize in non-lethal alternatives. You are the person paying for the service. Keep asking around until you find a company willing to give you what you want.
Remember, some states prohibit the translocation of wildlife. In those situations, the NWCO would have to install a one-way door. One-way doors can be effective but they also tend to be expensive due to the labor involved. However, a key advantage lies in the fact that the work would also prevent re-invasion of wildlife.
References:
The handbook for training nuisance wildlife removal companies in New York State
Tips for choosing a NWCO
Resources on Controlling Opossums
