If they are local, the EMC and safety labs usually will help with identifying the standards that apply and the appropriate tests. What they ask for and suggest is sometimes negotiable and open to discussion, depending on how unique your design is and how unfamiliar they are with it. For instance, noting that it's an amplifier without pointing out the 400V rail might lead them to a less stringent quotation than would happen if it was only 50V. They will find it in the review, and then all the sudden another standard and 20 more hours might be needed. A good Theory of Operation for the evaluating engineer will help with that.
The industrial projects I've seen go through EMC usually come in between $10,000 and $20,000. It depends on how complex they are, what connects to them, which global regions to cover, how many time you need to go back, etc. I don't do much with safety approvals but I suspect it's about the same. Perhaps with a simpler device it may be lower.
If in their consultations you get quotations, they will specify which standards and their revisions will be applied. Buy each one and study them. It isn't easy language to work with at times, and often one standard will draw on other standards. You may need to purchase those as well. They tend to cost in the $25 to $200 range, depending on length, obscurity, popularity, etc. Expect to get 2 or 3 for each of EMC and safety.
As for opening it up, security screws, safety labels, and warnings in the manual help with your side of the liability.
Here's a trap to watch out for: sometimes the solution for one makes the other worse. For instance, adding a capacitor to deal with EMC may cause a safety issue somewhere else. You can do EMC pre-testing of specific things without getting a report. I suspect that if your amplifier isn't loaded with a bunch of high speed digital circuitry, clocks, and radios then it's more of an immunity issue than an emissions issue. This suggests doing the safety tests first, then go to EMC. Any changes may require only limited retesting.