The Point are currently five points from safety but boss Barry Gray will be hoping his new additions can turn things around for them.
Hand, a 22-year-old defender, moves to Milltown after spells with Athlone Town, Dundalk and Longford Town, and Gray feels he is a "great fit" for Warrenpoint.
“Dylan is a great fit for what we are looking for, a great age, and he will add much needed depth to our defensive options," he told the club website.
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"I know Dylan is extremely talented and has already built much experience for a young player, he is keen to get in competitive action and establish his place in the team.”
Midfielder McKenna is Gray's second addition of the transfer window.
The Republic of Ireland youth international has had previous spells with Athlone, Shelbourne, and Wolves and the Point boss feels he can provide his squad with an immediate boost.
"Dan is our second addition and I’m really pleased to have him on board," said Gray.
"Dan is a player that is match fit and raring to go so we expect he can provide us with an immediate boost.
“We know we had to add depth to the panel in January."