Well, after much frustration I was able to grab all the dependencies myself.
They are:
Microsoft.NET.Native.Framework.2.2_2.2.29512.0_x64__8wekyb3d8bbwe.Appx
Microsoft.NET.Native.Runtime.2.2_2.2.28604.0_x64__8wekyb3d8bbwe.Appx
Microsoft.UI.Xaml.2.8.x64.appx
Microsoft.VCLibs.140.00.UWPDesktop_14.0.33728.0_x64__8wekyb3d8bbwe.Appx
Microsoft.VCLibs.140.00_14.0.33519.0_x64__8wekyb3d8bbwe.Appx
They can be downloaded using a MS Store catalogue such as store.rg-adguard.net where you can paste in the MS Store link for Shapr3D. The packages can then be installed locally using the command Add-AppxPackage -Path *.Appx.
The .msixbundle which Shapr3D provides can be extracted using regular unzip software and the appropriate .appx can be installed for your platform again using the command above.
I am still extremely frustrated that I had to go through this incredibly onerous manual process simply because the Shapr3D developers do not deign to distribute a regular installer for the program which works without the burdensome Microsoft Store being installed.
Now the program is installed and working but keyboard input does not work properly and therefore I can’t even get past the tutorial. Seriously, this ain’t cool.