A bit of math to help you with your choice.

A 165SR15 tire is approximately 25.6" tall. Technically, the metric SR tires' aspect ratio is 82% (165/82-15). To do the math take 165mm (section width) and divide by 25.4 to convert to inches = 6.49", then multiply by .82, the aspect ratio. You get 5.32". This is the sidewall height. Since you have a sidewall on the top and bottom, the height of the tire is the wheel diameter + 2x the sidewall height. (5.32 x 2) + 15 = 25.6" tall. A decent approximation of tire height.

If you go 195SR15 -- follow the same math -- you have a tire height of 27.6". That's going to throw your speedo off. (27.6-25.6)/25.6 = .078 -- or about 7.8%, let's call it 8%. So if your speedo is accurate with the 165 tires, when it says you're going 60mph with the 195's, your actual speed will be about 64.8, call it 65 mph.

More importantly, if your wheel width is actually 4", then the 165 is about the widest tire you'd want to put on that width wheel. Actually, a good rule of thumb is that you don't want a section width that is more than your wheel width + 2". Your wheel width is 4". So ideally you don't want a section width of your tire of more than 6" == 152mm. So, a 155SR15 tire would actually be a better fit for a 4" wheel. The 195mm section is much too wide for a 4". For tires that are equally sticky on the 4" wheel, you'd likely get better performance out of a 155 or 165 tire than you would the 195.

Additionally, that taller tire (effectively a "taller rear gear") will slow acceleration a bit. And, it's going to be heavier than a 155 or 165 tire - which will also slow acceleration.

Having gone into all that -- I'd look for a quality 155 or 165 section tire for a 4" wheel. If you insist on moving up to a 195 section tire -- keep the heights similar. That would be a 195/70/15. And for wheel width -- (195/25.4)-2=5.7". You'd want at least a 5.5" wide wheel, a 6" wide would be even better.