If you want to get as close to 115mm then I see two options.

The first is a custom stem that was already mentioned above.

The second is going 120mm with enough positive angle in rise instead of the 0 degree rise so that the horizontal length gets closer to 115. In the second case you'll need to remove steerer tube risers to account for the added rise of the stem.

Do you have risers between the stem and headset? If not, is there any steerer tube above the stem or is it already cut flush? What is the drop between the saddle and the handle bar? If you have too much drop (personal opinion here ... more than 4 cm is too much drop unless its a TT specific bike) then you might want to address that first and then correct the stem length.