There are several scripted DoWs in the game that generate a bit more or less than the standard amount of Threat, and Marco Polo Bridge is likely to be one of them, I haven't actually checked the numbers. Since Shanxi comes in automatically, they're a "freebie" for you, no additional DoW needed, and no extra Threat gained, and if China manages to draw in any of the other warlords, that's just one more for you to take without increasing your Threat with the US.
Also be aware that the scripted war goals can sometimes be counter-productive. As a prime example, Germany taking the "Vichy" option as the default means that they get the rich northern part and coasts, convert the south into an independent state under German protection, and leave the scattered pieces of the French empire to continue the fight on the Allied side. A human-controlled Germany can instead decide to annex ALL of it, or else can take only the rich north and puppet the rest, instantly bringing any remaining French divisions and the French fleet into the Axis. No need to garrison the southern half of the Atlantic coast, the Med, and all of those scattered French possessions around the world if France will do it for you. The down side is that most of that French land in Africa and Asia will then be vulnerable to UK attacks, and France's National Unity will be low, so you may need to support them if the UK/US make any serious landings on the continent.
In your case, check your options before deciding to initiate "Marco Polo" or to choose the "Take the Coasts" war goal; it may or may not be a good idea, depending on your long term objectives, and it may or may not pay to simply declare war instead of following the historical path. If one warlord is allied to 4 others, a DoW on that warlord will likely put you at war with all 4 of the others, with only the Threat for the one original declaration....assuming that you feel capable of taking on all of them at once.
Another example: After CZE, the UK guarantees Poland, and Poland in effect becomes an Allied member (the latter situation not being very historical). By declaring war on a neutral country (HUN, YUG, HOL, DEN, BEL, etc.), it puts GER's Threat on the UK over the limit, and the UK will declare its own war in a matter of days. That gives GER its desired war with Poland and France, plus that neutral country, with only one DoW, instead of having to DoW that neutral seperately. Basically, the UK gets the blame for starting WWII, or at least escalating it from a local war into a "world war".
Also be aware that the scripted war goals can sometimes be counter-productive. As a prime example, Germany taking the "Vichy" option as the default means that they get the rich northern part and coasts, convert the south into an independent state under German protection, and leave the scattered pieces of the French empire to continue the fight on the Allied side. A human-controlled Germany can instead decide to annex ALL of it, or else can take only the rich north and puppet the rest, instantly bringing any remaining French divisions and the French fleet into the Axis. No need to garrison the southern half of the Atlantic coast, the Med, and all of those scattered French possessions around the world if France will do it for you. The down side is that most of that French land in Africa and Asia will then be vulnerable to UK attacks, and France's National Unity will be low, so you may need to support them if the UK/US make any serious landings on the continent.
In your case, check your options before deciding to initiate "Marco Polo" or to choose the "Take the Coasts" war goal; it may or may not be a good idea, depending on your long term objectives, and it may or may not pay to simply declare war instead of following the historical path. If one warlord is allied to 4 others, a DoW on that warlord will likely put you at war with all 4 of the others, with only the Threat for the one original declaration....assuming that you feel capable of taking on all of them at once.
Another example: After CZE, the UK guarantees Poland, and Poland in effect becomes an Allied member (the latter situation not being very historical). By declaring war on a neutral country (HUN, YUG, HOL, DEN, BEL, etc.), it puts GER's Threat on the UK over the limit, and the UK will declare its own war in a matter of days. That gives GER its desired war with Poland and France, plus that neutral country, with only one DoW, instead of having to DoW that neutral seperately. Basically, the UK gets the blame for starting WWII, or at least escalating it from a local war into a "world war".