Is it possible without deleting the field?

Yes, it is possible. I found a very simple solution while searching.

I will show you the code, and some explanation, and then provide you with a link to the source.

This solution can be applied to all fields, you just need to adjust for how they are setup in the database.

function MYMODULE_update_7001() {
  // Manual database changes to the field config table. Sometimes there is serialized data to take into account.
  db_query("UPDATE {field_config} SET type = 'number_integer', module = 'number' WHERE field_name = 'field_name'");
  // Text fields have an aditional column for format which number doest have. We drop those.
  db_query("ALTER TABLE field_data_name DROP field_name_format");
  db_query("ALTER TABLE field_revision_name DROP field_name_format");
  // Change all empty values to 0 otherwise we get an error.
  db_query("UPDATE field_data_name SET field_name_value = '0' WHERE field_name_value =''");
  db_query("UPDATE field_revision_name SET field_name_value = '0' WHERE field_name_value =''");
//change the default values
  db_change_field('field_data_name', 'field_name_value', 'field_name_value', array(
    'type' => 'int',
    'length' => 11,
    'not null' => FALSE,
    'default' => NULL
  ));

  //revision field
  db_change_field('field_revision_name', 'field_name_value', 'field_name_value', array(
    'type' => 'int',
    'length' => 11,
    'not null' => FALSE,
    'default' => NULL
  ));

  field_cache_clear(TRUE);
}

Notice in the above the writer does both the field and the revision field. This is critical to get both fields.

After you have created your module and deployed it, you can run update.php for the hook_update() to work.

The full blog can be found here.