Yes, you can. You don't have to have a wake/funeral service if you don't want to. I have also looked into this. There are 2 ways you can do this.
1. The first is if you don't want a wake/funeral service at all. You would have a meeting with a funeral director. You tell him that you want to pre-pay for your funeral. Tell him that you want a Direct Burial or a Direct Cremation. This means that after your death, the funeral director will arrange to have you buried or cremated immediately. There won't be a wake/ funeral beforehand. You have to pick out your coffin or urn ahead of time, sign a contract, and prepay. I have looked into this. It is perfectly legal to do so.
2.The second option is you can request To have a private funeral service. You write a list of all the people you want at your funeral and print out the invitations ahead of time. You would also have it written in your obituary that there is going to be a private service- by invitation only. You could arrange this with a funeral director ahead of time and pre-plan your funeral. You could also discuss this with a relative or close friend ahead of time, if you think you could trust them, and they would respect your wishes. A friend of mine had a private funeral a few years ago. She arranged it with the funeral director ahead of time. The only people allowed were members of the immediate family and a few close friends. No one else was allowed to enter.