Honestly, it is not much of an upgrade. The coffee lake CPUs only have about a 5-10% performance increase over Haswell and the 8100 is only clocked a few MHz higher than your 4440. I would not make the change as you will not see much improvement and you will still need to buy a motherboard and RAM.
As for bottlenecking your 960, no it wont in most games. But in CPU heavy games, such as BF1, you will be under the minimum requirements and there will be some issues. If I were you, I would look at spending an extra $50 and get the 8400 as it will be a better upgrade.