Adding a stick to an image

I have read so many articles and am still completely confused! I want to make some swizzle sticks for cocktails. I am trying to take my images and add a swizzle stick base (file purchased from Etsy) to it. I cannot simply combine the two files without the outlines cutting them apart. I use Inkscape and then upload to Glowforge. It seems like it should be a simple process but I cannot figure it out.

In Inkscape, chose the shape and the stick, then select path, union.

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I must be doing something wrong because that never works for me.

They must be vector shapes, either objects or paths - either works.

If they are not vectors Gimp makes it even easier than Inkscape. I was converting extended textures to vectors before joining them (like using union) but have found myself staying in raster format to multiply the pattern and then setting it to vectors.

Or if you have Glowforge Premium, just position them however you like and apply a 0.0 Outline to them. Obviously you would then ignore the two individual cut lines and only cut the outline.