96 Speedster? Eh?
Well, that would be a 2 stroke motor. And so smoke means either OIL or WATER. If it is water, then it is steam, which would be normal, if somebody got water in the exhaust system. Oil? Could be a bunch of oil in the bottom of the motor.
I say, run it for an hour, and then tell us what is going on. I mean, ride it. If it clears up, then you just may be ok. Get her heated up, and the system cleaned up. Another source of "smoke" or steam, could be lots of ETHANOL in your gas, has sucked up water out of the air, and now, she has a bit of water to run out.
I am having issues with a 24 HP industrial Honda motor on a sawmill, right now, due to this very issue. I will have to DUMP out all the old fuel, and fill the tank with FRESH fuel, to the full.
I was following a NEW car the other day, and it was DUMPING water out of one side of the dual (probably fake dual) exhaust, when the driver went up hills, and pressed the accelerator a bit. All I am saying is that it would not hurt to look at the bigger pic of this issue. It may not cost you money in repairs, but you may need FRESH gas.
Also, if this motor has the rotary gear on the bottom, end, then it could be a bad rotary gear seal. To check this, remove the spark plugs, ground the spark plug wire, and crank it over, and see if it spits a wad of oil out of the spark plug hole.
As always, if you need to use jumper cables, do not have the HOST engine running, although this is standard for cars, and normal equipment. You can mess up the electrical system if the HOST in a jumper situation is RUNNING.
Also, Mr. Plough5757, that pic is just a bit lewd. My kids came in, and I was ashamed to have that on my screen. Do you mind changing it?
Thanks!
Nate