No, no it won't. 243 using 105 hyb at 3050 fps VS your typical Tikka 65cm load at 2720fps with a 140, same wind. Cept at 700y the 243 is still 200fps faster. The 243 is easier to shoot as well. A 243 can push the 105s faster, and if you go 7.5tw, there are a lot better bullets than the 105. Unfortunately, Tikka barrels are notoriously slow, especially if you start shortening them. You have to dump rl26 in em to get the velocity that normal powders get in a quality cut rifle tube. Yes they do last a long time tho.The 6.5 will have less wind drift than the .243.
Op should buy a quality barrel and have a smith fit to his Tikka 308 action in 243 or 6cm 7.5tw, and shoot 108 Berger, 109 eldm, or 112 match burners at 2950-3050 fps, all totally doable from a 22" barrel at moderate psi levels. Buy an action wrench and a barrel vise, torque wrench, and have your own switch barrel setup.