可以使用递归函数实现遍历并删除所选对象的字段。以下是一个简单的实现示例：

import json

def delete_field(obj, field, value=None):
    """
    递归函数：遍历JSON对象/数组并删除所选对象的字段
    obj: JSON对象或数组
    field: 要删除的字段名
    value: 如果指定，则只删除字段值等于给定值的对象的字段
    """
    if isinstance(obj, dict):
        # 如果是字典，遍历所有键值对
        for k, v in obj.items():
            if k == field and (value is None or v == value):
                # 如果找到了要删除的字段，将其删除
                obj.pop(k)
            else:
                # 否则，递归调用自身
                delete_field(v, field, value)
    elif isinstance(obj, list):
        # 如果是列表，遍历所有元素
        for i, v in enumerate(obj):
            if isinstance(v, (dict, list)):
                # 如果是字典或列表，递归调用自身
                delete_field(v, field, value)
            elif i == field and (value is None or v == value):
                # 如果找到了要删除的字段，将其删除
                obj.pop(i)

# 示例用法
data = '''
{
  "name": "John",
  "age": 30,
  "hobbies": ["running", "reading", "swimming"],
  "address": {
    "street": "123 Main St",
    "city": "Anytown",
    "state": "CA",
    "zip": "12345"
  }
}
'''

# 将JSON字符串解析为对象
obj = json.loads(data)

# 删除address字段
delete_field(obj, 'address')

# 删除hobbies列表中值为"reading"的元素
delete_field(obj, 'hobbies', 'reading')

# 将修改后的对象重新转化为JSON字符串并输出
print(json.dumps(obj, indent=2))