Delete a given node in Linked List under given constraints

Given a Singly Linked List, write a function to delete a given node. Your function must follow following constraints: 
1) It must accept a pointer to the start node as the first parameter and node to be deleted as the second parameter i.e., a pointer to head node is not global. 
2) It should not return a pointer to the head node. 
3) It should not accept pointer to pointer to the head node.
You may assume that the Linked List never becomes empty.
Let the function name be deleteNode(). In a straightforward implementation, the function needs to modify the head pointer when the node to be deleted is the first node. As discussed in previous post, when a function modifies the head pointer, the function must use one of the given approaches, we can't use any of those approaches here. 
Solution 
We explicitly handle the case when the node to be deleted is the first node, we copy the data of the next node to the head and delete the next node. The cases when a deleted node is not the head node can be handled normally by finding the previous node and changing the next of the previous node. The following are the implementation. 
 

Output: 
 

Given Linked List: 12 15 10 11 5 6 2 3

Deleting node 10:
Modified Linked List: 12 15 11 5 6 2 3

Deleting first node
Modified Linked List: 15 11 5 6 2 3

TIme Complexity: O(n)

As we are traversing the list only once.

Auxiliary Space: O(1)

As constant extra space is used.

Please write comments if you find the above codes/algorithms incorrect, or find other ways to solve the same problem.