If you don't want to test your procedure, you probably haven't written it well enough. Have someone with a limited knowledge of the process (or a person representative of the normal reader) use your SOP to guide them. What issues did they run across? If any, address them and make the necessary improvements.  It's best to have a handful of people test your SOP. Different individuals will have different issues, allowing for a wide variety of (hopefully useful) responses Be sure to test the procedure on someone who's never done it before. Anyone with prior knowledge will be relying on their knowledge to get them through and not your work, thus defeating the purpose. At the end of the day, it doesn't really matter what your bosses think of the SOP. It's those who actually do the work that it matters to. So before you submit your work to the higher ups, show your stuff to those that'll be doing (or that do) the job. What do they think? Allowing them to get involved and feel like they're part of the process will make them more likely to accept this SOP you're working on. And they'll inevitably have some great ideas! Once the team gives you the go ahead, send it to your advisors. They'll probably have less input on the actual content itself, but they'll let you know if it meets formatting requirements, if there's anything you missed, and the protocol for making it all official and input into the system.  Route the SOP for approvals using document management systems to ensure audit trails of the approvals. This will vary from organization to organization. Basically, you want everything to meet guidelines and regulations. Signatures will be necessary and most organizations nowadays have no problem accepting electronic signatures. This may involve executing a formal training for the affect personnel (e.g. classroom training, computer-based training, etc.) or it may mean your paper is hung up in the bathroom. Whatever it is, get your work out there! You worked for it. Time for recognition! Be sure your SOP remains current. If it ever gets outdated, update it, get the updates re-approved and documented, and redistribute the SOP as necessary. Your team's safety, productivity, and success matter on it.
Test the procedure. Have the SOP reviewed by those who actually do the procedure. Have the SOP reviewed by your advisors and the Quality Assurance team. Once approved, start implementing your SOP.