I second using Photoshop. Simply export the sequence you want to work as a normal video. Then import that video into Photoshop - it will bring up the Animation Timeline so you can edit frame by frame. Photoshop can import video and edit it frame by frame. To limit the smoothing effect to just the skin, add a layer mask. Hold Alt/Option while clicking on the Add Layer Mask tab at the bottom of the panel. A black-filled layer mask thumbnail appears on the “Smooth Skin” layer.
In Photoshop there is a smoothing option in the brushes dialog which can somewhat smooth a brush stroke as you apply it, but probably not enough to smooth out the jitters caused by using a mouse. A graphics tablet like a Wacom would be a better input device. And it is possible to draw smooth Bezier curves with the Pen Tool and then adjust them later, and apply a stroke to it.
However, ultimately, Photoshop is really the wrong kind of software for what you are trying to achieve. Adobe Illustrator a is vector image editor, and is more suitable for line art and illustration. In Illustrator you can adjust the smoothness and fidelity of the Brush Tool. Also after you have drawn the line, then you can do further adjustments to the Bezier curves. In Adobe Illustrator, here's an example of a line drawn with the Brush Tool, using a mouse, with smoothing applied, also showing the Bezier controls. Similarly here is an example of a vector line drawn in Photoshop with the Pen Tool (set to 'Shape' in the options) with a stroke applied, and no fill applied. Similarly I also show the Bezier controls.
I also used a mouse to create this. Note: although Photoshop has basic vector capabilities, it's not comparable to Illustrator which was designed for that purpose.
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Another example of what's possible with Illustrator, again drawn with a mouse. Illustrator makes such beautiful and perfect curves and strokes with such little effort.