I have printed the waterdrop shape on the cardstock. I want it to have sharp and smooth edges. I'm not an artisan at crafts, however, scissors and utility knife leave a lot of roughness.
If you have a makerspace in your area or a similar craft related activity/club, you may be able to gain use of a craft cutter such as the Silhouette Cameo or a Cricut product. Still associated with the makerspace, you may find members with a laser cutter. Stretching the application a bit means you could also use a flatbed CNC machine to make the straight and large curves, although the small point at the bottom would have to be done by hand with a sharp craft knife.
I've recently become aware of a product that can be best described as a high-frequency vibrating craft knife. At a cost of US$399, it's steep for hobby use, but might be practical for high production craft use. It's a Kickstarter campaign called Wondercutter, but as a Kickstarter item, there's a risk involved.
As I own a laser cutter which cuts cardboard quite cleanly, it's on the top of my suggestion list.
Xacto knife is the artist standard for cutting mats when mounting pictures. Mats are made from a very thick cardstock. You already have the stencil, you may want to get a French Curve ruler. That helps with stability while cutting.
LINKS See the xacto website for knives & blade options. There’s a wiki link about french curves. Also an article about mat board and different thicknesses of cardstock as well as foamcore board.