You can use the blending modes on the Layers Panel.
But this guy on the picture must have a face and you won't have choice to "cut out" either the layer with the color or parts of the picture at some point if you don't want the subject to have a blue skin. Otherwise you'll need to use a brush to apply your blue color on a new layer.
The blending modes can help but they cannot do a perfect result if you don't separate the background from the subject. And the color will never be as saturated as you want.
Luminosity blending mode
Color blending mode
Overlay blending mode
Mix of blending modes and layer masks
Using the layers masks would greatly help you get closer to these colors and adjust separately the background and the shirt. I know you mentioned you don't want to cutout the picture but not using layers masks is like not using shortcuts; you can manage without them but your life will be much easier and projects done faster if you use them!
This is just a crude example but you should make your own tests and experiment with layer masks and blending modes.
You can also use Layer Adjustment instead of layers the way I did. There's some good info on Blending here.