First time with stranger.......

Only speak when spoken to. Don't play out of turn. If you are having a bad hole, just politely pick up your ball so as not to delay him, and recommence on the next hole.

Or, just chill out and realise he is just another person who will most likely be happy he has someone to play golf with. Just play your own game, and if you don't follow the rules, who cares. It is just a friendly practice game, not a comp or score to be submitted for handicap. Just because he plays off 9.5, don't assume he thinks he is a class player and you are inferior. I'm lower than that, and I'm garbage. I don't care if I'm playing with a low or high handicapper. I often play with a guy who is almost off 30 and worst ball striker I've ever seen. Who knows, the 9.5 handicapper may feel more relaxed playing with you that he would with a lower handicapper than him?

Second option is best. 99% chance he'll be fine to play with, and even a chance you guys end up playing many times in future. Many of my long term social golfer friends (and even friends off the golf course in some cases) were first met randomly during a round of golf.
 
Just relax and enjoy it. You both want to enjoy the round, after all.
Friendly advice though. I dont believe you should be making up your own rules at this stage, or indeed any stage of your playing career. This sets bad precedents which may be difficult to shake off later when you start playing competitively. Then, if you are caught playing 'your rules', you may find that you have no one to play with, and a bad reputation.
 
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