50t / 38t Shimano Zee crankset double 10 speed casette old mountain bike commuter conversion
Length of chain does not matter. The issue you will face is the rear derailleur's total capacity. Basically it's rear derailleur's ability to take up chain slack.

Total capacity = (difference in tooth count of front rings) + (difference in tooth count of largest and smallest cassette sprockets)

You can see the size of the biggest ring is not an issue, it's the difference between the two rings that counts. 50-38 38 is 12, which is less than standard road bike difference of of 16 (52-36, 50-34 etc.) so you should be fine with long cage derailleur.