I think you will have problems. A firmer ride would be the result of a stiffer spring and not the shock unless the shock is over-damped but in this case the shocks have a fixed damping ratio which is optimized based on the spring rate and weight of the car, etc. So basically a shock is tailor designed for a particular spring. If you change the spring rate, you have to change the damping rate to get the desired performance and vice versa. This means that sport struts and non-sport struts have different damping rates because the spring rates for each setup will be different. Can you mix springs and shocks? Yes... Is it ideal? No... Will it change suspensions characteristics? Absolutely but not necessarily for the better.
The other thing to consider too is that sport suspensions are lower by about an inch therefore the sport struts would have about 1" less available travel than the standard strut. So they may not be long enough, but I'm not sure about that. If you purchased from a local retailer you could compare the lengths of the 2 part numbers to confirm this.
I have also read that using the incorrect length strut for the spring setup can cause premature failure of the strut. Their argument was basically the strut is designed to be compressed to a specific optimal position when weighted by the car. Depending on the springs used, this will be a different position which is one reason there are different shocks for a certain spring. Not sure how valid this is, but its what I have been lead to believe.
The other thing that could be an issue is that sometimes struts are a spring and shock assembly. Not sure if this is the case with these struts but if it is, you will have issues mixing a sport designed strut assembly up front and stock spring/shocks in the back. The images online suggest it is just the strut and doesn't come with a spring.
Also your new strut warranty will be void since the application is not correct, if something happens with regard to your suspension like premature failure or control arm issues or whatever it would be on you unfortunately.
If it were me, I would play it safe an return for the correct part number.
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