I found a satisfying solution.
I tried to import font using @font-face, but this doesn't work for me, because multiple @font-face for each "style" (italic, bold, bold+italic) was not recognized by wkhtmltopdf. I had to use a "free" font ("DejaVu Sans" in my case) that was available on my Windows system and on the Linux Server and is directly available by the system when it generates the PDF.
Those two fonts now renders similarly between my Wisywig and the PDF generated. I also had to use a lot of CSS rules to make it clean, removing PNG images ... but that's another story.