You need to separate chainline from spindle length because they don't equate. Chainline is the distance of the chain's central line from the frame. Ideally you want the mid point of the chainrings to line up with the mid point of the cassette, so the chain is running as close to staight as possible in the most common combinations.
Most road and "trekking" cranks are designed for a 45-47 mm chainline. Mountain bike cranks are designed for a 50mm chainline. If you put a mtn bike crank on the BB you just had the road crank on, it will not fit. I use Sugino mtn bike cranks when building up touring bikes, I use a 103mm bottom bracket to get the correct chainline, because I like STI shifters.
IMO- I'd work with adjusting my chainline in by using the correct size BB. I think you are on the right track. Measure your chainline with the
new crank on the old bottom bracket. subtract 46 mm from that measurement. Double the resulting number, and subtracting it from your old BB size should give you the correct BB length, e.g., 54 mm from center of seat tube to middle chain ring with a 118 mm BB. 54-46= 8, 8 x 2= 16, 118 (or whatever size you have)-16= 102mm. From your measurements it seems like you want a BB 16 mm shorter than the one presently on your bike. This assumes you have a 68 mm BB shell.
In the product description, it seems like they recommend a 110 mm for a 50 mm chainline. If you want to pull it in to 45-47 then you need down to the 103 mm BB which I found to work well with mountain cranksets installed on road bikes.
Greasing a square taper BB spindle is NOT recommended.