Will wire unequivocally add too much ESR or inductance to the whole? No.
In many situations, such as bodge-testing a beta design with more capacitance, a tiny bit of wire of the appropriate diameter will only add several or tens of miliOhm to the total resistance and usually inductance is limited.
However, should you use this solution of yours? No again.
Or to put it in terms of an answer to one of your latest comments:
Actually ordering the original replacements and waiting for them, on the other hand, will save you the potential hassle of buying a new laptop.
A capacitor of which the legs break is not to be trusted. Those legs are spot welded (or whatever they use as a process the last few years) onto the alu-foil, so the torsion is likely to misalign aluminium foil or even short it or warp the stack-up, before the leg breaks.
This can have detrimental effects to any one of the specifications, if not all of them. A 5% to 10% error in most specifications should be allowed in the design, if the designer understands his actual job. An error of 10% in all of the specs, or a 40% error in one, on the other hand, is a whole different story.
Look at it like this: If you order the caps, put them in without destroying anything else and then it works again, you spent 3 days waiting and a buck or three. If you do it like this you have a chance of being out an entire laptop in trade for 3 days quicker. In which case those 3 days won't have made a damn of a difference on the following decades of no laptop.