You haven't said whether your 2008 Specialized is road or MTB. But if your existing bike is a road bike, you might want to look at the article at the link below. Per that reliable source, Shimano MTB and road front derailleurs have different pull ratios.
https://bike.bikegremlin.com/1297/bi...mpatibility/#6
I've read that elsewhere as well, so I'm pretty sure that's accurate.
If your 2008 Specialized is a MTB and your FD is Shimano, using Shimano MTB shifters of the proper type (double or triple) should be no no problem. But if it's a road bike, theoretically you might have issues if you "mix and match".
Can't say from personal experience one way or another; haven't ever replaced road FD shifters with MTB FD shifters.