Write a Python function `trim_tuple` that takes a list of tuples and an integer `k` as input. The function should return a new list of tuples where each tuple is trimmed by removing `k` elements from both the beginning and the end. If `k` is greater than or equal to half the length of a tuple, the resulting tuple should be empty.
#### Example Usage
```python [main.nopy]
# Example 1
input_list = [(5, 3, 2, 1, 4), (3, 4, 9, 2, 1), (9, 1, 2, 3, 5), (4, 8, 2, 1, 7)]
k = 2
print(trim_tuple(input_list, k))
# Output: [(2,), (9,), (2,), (2,)]
# Example 2
input_list = [(7, 8, 4, 9), (11, 8, 12, 4), (4, 1, 7, 8), (3, 6, 9, 7)]
k = 1
print(trim_tuple(input_list, k))
# Output: [(8, 4), (8, 12), (1, 7), (6, 9)]
```
#### Constraints
- The input list will contain tuples of integers.
- The value of `k` will be a non-negative integer.
- The function should handle edge cases, such as empty tuples or `k` being larger than the tuple length.