How to Get Wishlist ID According to Product ID in Magento

Try to override core classes Mage_Wishlist_Model_Resource_Item_Collection and Mage_Catalog_Model_Resource_Product_Collection according to diff:

Mage_Wishlist_Model_Resource_Item_Collection

@@ -184,9 +184,13 @@
         $this->_productIds = array_merge($this->_productIds, array_keys($productIds));
         $attributes = Mage::getSingleton('wishlist/config')->getProductAttributes();
-        $productCollection = Mage::getModel('catalog/product')->getCollection();
+
+        /** @var Mage_Catalog_Model_Resource_Product_Collection $productCollection */
+        $productCollection = Mage::getModel('catalog/product')->getCollection()
+            ->setUseLeftJoinForPriceIndex(true);
+
         foreach ($storeIds as $id) {
-            $productCollection->addStoreFilter($id);
+            $productCollection->addWebsiteFilter(Mage::app()->getStore($id)->getWebsiteId());
         }

         if ($this->_productVisible) {

And Mage_Catalog_Model_Resource_Product_Collection:

@@ -132,13 +132,20 @@
     protected $_productCountSelect           = null;

     /**
-     * Enter description here ...
+     * Is website filter
      *
      * @var bool
      */
     protected $_isWebsiteFilter              = false;

     /**
+     * Type of joining price index table
+     *
+     * @var bool
+     */
+    protected $_useLeftJoinForPriceIndex     = false;
+
+    /**
      * Additional field filters, applied in _productLimitationJoinPrice()
      *
      * @var array
@@ -1759,11 +1766,15 @@
     /**
      * Join Product Price Table with left-join possibility
      *
+     * @param bool|null $joinLeft
+     *
      * @see Mage_Catalog_Model_Resource_Product_Collection::_productLimitationJoinPrice()
      * @return Mage_Catalog_Model_Resource_Product_Collection
      */
-    protected function _productLimitationPrice($joinLeft = false)
+    protected function _productLimitationPrice($joinLeft = null)
     {
+        $joinLeft = is_null($joinLeft) ? $this->_useLeftJoinForPriceIndex : $joinLeft;
+
         $filters = $this->_productLimitationFilters;
         if (empty($filters['use_price_index'])) {
             return $this;
@@ -2172,4 +2183,18 @@

         return $this->_pricesCount;
     }
+
+    /**
+     * Set type of joining price index table
+     *
+     * @param bool $value
+     *
+     * @return Mage_Catalog_Model_Resource_Product_Collection
+     */
+    public function setUseLeftJoinForPriceIndex($value)
+    {
+        $this->_useLeftJoinForPriceIndex = (bool)$value;
+
+        return $this;
+    }
 }

Unfortunately Magento didn't provide ready to use function to delete item from wishlist. But you can use follow code to do this, I tested it and all works fine at my local Magento.

protected $wishlist;

public function __construct(
    \Magento\Wishlist\Model\Wishlist $wishlist
) {
    $this->wishlist = $wishlist;
}

public function execute()
{
    $customerId = 1;
    $productId = 6;
    $wish = $this->wishlist->loadByCustomerId($customerId);
    $items = $wish->getItemCollection();

    /** @var \Magento\Wishlist\Model\Item $item */
    foreach ($items as $item) {
        if ($item->getProductId() == $productId) {
            $item->delete();
            $wish->save();
        }
    }
}