I don't think the breeds make much difference. Early socialization is far more important. At family get togethers, we have 3 Labs, a Shepherd, a terrier mix, and a Fox Hound. The Fox Hound came from a shelter and doesn't get along any of the other dogs. The other 5 have a good time together. They were all carefully socialized to both dogs and people while quite young.
The percentage play is one male and one female. Usually any 2 dogs will do fine together. When there is a problem, 2 females are the most likely case.
I also agree that breed will likely not cause problems...lack of training and socialization will. Yorkies are terriers and corgis are herders. Both may be prone to being hyper. Given the proper exercise, you should be fine.
Being a woman myself I think this is true for most mammals
Anyway spaying usually helps if not fixes this problem completely. Same can happen with two highly driven males. Again, neutering will help if not fix it.
It is also important to train dogs. My in laws have two females and one is a terror. They are just lucky that their pit mix is just an old angel that doesn't get jealous. My Luna (terrier mix) and my gentle Spyro (doxie mix) cannot be around their Princess (rat terrier) due to the fact that...well she thinks its ok to misbehave. This has led to Spyro snapping at her (which is rare for Spyro) and Luna fighting her. Besides the fact that she doesn't get along with any other dogs (besides the old pit bull and the new puppy which is also madly untrained) she drives visitors nuts by snapping and jumping on them.
As long as you get both dogs young (8-10 weeks) preferably then they should definitely have no problems! I am sure they will get along and become each others buddies and play and snuggle! Be sure to socialize both dogs with people and other dogs outside your home so they can have the best life possible and the best outlook on life possible! Good luck!