oh ive had this at the salon. One thing i can say is dont feel embarrased by ur child screaming, we actually feel more embarresed than u do and wonder why they kid hates us so much. I had to cut a boys hair not long ago and it was his first haircut. I think he was about 2. He didnt like the idea of it at all but i turned him around. I let him use one of the spray bottles to play with and my god the place was soaked by the end but his hair was cut. Some kids love haircuts and some think its murder. Theres not much u can do really. Alot a praise will help. Even if u say to him "we will just do a little bit and then we will go" and then when she does a little bit say "oh look at you, ur beautiful, im so proud of u" it may sound abit silly but ive done this and it works. Also i used the tecnique to think they are in control. Saying things like "u let me know when u are ready and we will do a little bit more" and "u just tell me when to stop when u want to have a break", they do think they are more in control if u give them the option. Given ur bub is only 15 months old he may not pay attention to anything u say because he is just terrifed. So the distraction thing is the best i would think.
Have u thought about hunting around for a home hairdresser? one that comes to ur home? he might not feel as threatened if hes at home.

sorry to ramble... HTH