Practice and become decent at taking some of the most-useful and efficient shortcuts. Getting good at shortcuts such as gap-jump on Mushroom Gorge, shroom/shroomless on Bowser Castle 3, double on Delfino Square, double on DK Summit, ultra on Dry Dry Ruins, and so on will help greatly in the long-run with breaking away or keeping up and/or catching up to the pack if you fall behind.
I also recommend learning how to read the map, as it will aid in terms of predicting when shock may occur for the potential dodge. In WW's, people typically chain shock into an item-set, so knowing where every item set is on the map and keeping an eye on where the bottom-spots people are in proximity to those item sets will improve your chances at predicting the shock.
For clan wars, the shock typically occurs in 4 different scenarios: target shocks, chain into an item set, canon or other invincibility frames dodges, or at random.
Target shocks are likely the easiest and most-obvious to predict, and holds a lot of potential to dodge the opposing team's shock. When one of your top-placement teammates is coming up to a gap, especially on lap 3, it may very well be worth it to use your dodge item. If you are the one in a top-placement, try slowing down a bit before the gap. Know that the person holding the shock is watching your icon on the mini-map, try to make it more difficult for them to target shock you. However, this shock strategy is a double-edged sword, as you predict the other team to use the shock just as much as they predict you to use your dodge.
This follows closely with canon dodges and lava re-spawn dodges in terms of predictability. Tracks such as Maple Treeway, DK Summit, and DK Jungle Parkway are notorious for being utilized for canon dodges; and the team whom obtains the shock first holds the highest potential for getting the better placements. If you are on the team who does not have the shock, your teammates will usually exclaim that they will "get into canon" with the other team's players. This either prevents the other team from using the shock, or renders the shock less-useful as it dodges members of both teams. Keeping an eye on when the other team is approaching the canon and using your dodge before they enter will give you a higher chance of dodging.
Predicting an item-set chain in a clan war works very similarly to predicting an item-set chain in a WW. When lower placements are approaching an item-set, it may be worth it to use your item, again especially if it is lap 3. This one is less predictable than the former 2 however, as there is typically no certainty to which item-set the other team will chain at. Keep an eye on the opposing team's members who are around you and hover over the item-button to use your dodge as fast as possible. Coordinated shocks happen quickly, so you need to either predict through chance, or be quick to use your dodge item as soon as the opposing team uses theirs. If your teammates are in possession of multiple dodge items, a strategy that can also be used is to alternate the dodge items as to either prevent the opposing team's shock from happening, or rendering it less-damaging.
Finally, opposing teams may also choose to use the shock at random. As what randomness implies, this is obviously the most-difficult to predict. This shock strategy is not as much for the benefit of the team whom used the shock as it is a preventative measure to ensure that the other team does not dodge, and also loses their dodge items. Much similarly to the above, try your best to use your dodge item as soon as you see the opposing team's members in theirs.
Through this tsunami of text I really only listed two areas to attempt to improve upon; but there's a lot more to it than just shortcuts and predicting the shock. I know it's not exactly what you were looking for, but the majority of it really does boil down to
experience. Knowing proper lines to take, knowing how to chain items effectively, knowing the most-useful locations to use a golden mushroom or triple mushrooms, knowing where your teammates are, proper communication and chemistry with your teammates, and so on all comes from experience playing.
Everyone in this community has started somewhere; and the majority have improved and moved up to higher-division play over time. I think you should definitely try to work on shortcuts and shock-prediction if you haven't already; but honestly I also think you should try to just war as much as you can, as well. Work with your teammates, get to know them, ask for advice where needed, build a relationship and connection with them; and you will likely see improvement in your play over time.
Good luck.