As long as all the rules of spiritual weapon are observed, you are simply reflavoring the spell for fun - no harm done.
But to be clear, you must understand that this has no interaction whatsoever with mechanics such as two-weapon fighting (which means you can add your spell casting ability modifier to the damage!) or anything that says "melee weapon attack", you are still making a melee spell attack.
The other thing you must be aware of is how the spiritual weapon moves in relation to you. If you are moving and want to keep it with you, you must expend your bonus action to carry it with you, and it can only move 20 feet.
Also, you must be aware that spiritual weapon and shadow blade both have a casting time of one bonus action, so it would take two turns to set up your combo, after which you may use your action to attack with your shadow blade and your bonus action to move and attack with your spiritual weapon.
Now if you really want to commit to this particular style (which sounds like a lot of fun!), with a Dexterity score of 13 or higher, you can take the feat Defensive Duelist:
When you are wielding a finesse weapon with which you are proficient and another creature hits you with a melee attack, you can use your reaction to add your proficiency bonus to your AC for that attack, potentially causing the attack to miss you.
Shadow blade meets the conditions of this feat (emphasis mine):
It counts as a simple melee weapon with which you are proficient. It deals 2d8 psychic damage on a hit and has the finesse, light, and thrown properties (range 20/60).
While wielding your shadow blade, you would be able to use your reaction to add your proficiency bonus to your AC, potentially causing an attack to miss, which would help preserve your concentration on shadow blade.