Representing a many-to-one relationship in a database diagram
transactionID in loadingDetail can be duplicated when the loadingID
  different


This is your requirement.Table composite key already handling this.


  transactionID in stowageDetail is UNIQUE


This is your requirement


  •many transactionID in loadingDetail just can have 1 transactionID in
  stowageDetail


This is your requirement.This can Unique index. Or it can be handle via code/trigger.
This can never be FK constraint.You cannot define partial FK constraint.


  •transactionID in loadingDetail can be deleted when there is no
  transactionID in stowageDetail (No Action)


Because you cannot define partial FK constraint. You have to handle this via code.**Instead of Trigger** is ideal for this scenario.

I assume you cannot define transactionID and loadingID as FK in stowageDetail table because of your requirement.

Read this

As per your requirement, your design is already ok.Adding any other candidate key is useless. you cannot do it via PK-FK constraint.