Try downloading wheel with wget

This is not a usable solution, but it is useful for troubleshooting.

Author: EliahKagan

.github/workflows/cygwin-test.yml

@@ -30,22 +30,14 @@ jobs:
     - name: Install Cygwin
       uses: cygwin/cygwin-install-action@v4
       with:
-        packages: python39 python39-pip python39-virtualenv git
+        packages: python39 python39-pip python39-virtualenv git wget
         add-to-path: false  # No need to change $PATH outside the Cygwin environment.
 
     - name: Arrange for verbose output
       run: |
         # Arrange for verbose output but without shell environment setup details.
         echo 'set -x' >~/.bash_profile
 
-    - name: Add PyPI hosts file entry  # NOTE: Actually edits the Windows hosts file.
-      run: |
-        echo '199.232.96.223 files.pythonhosted.org' >>/etc/hosts
-
-    - name: Show hosts file
-      run: |
-        cat /etc/hosts
-
     - name: Special configuration for Cygwin git
       run: |
         git config --global --add safe.directory "$(pwd)"
@@ -71,6 +63,7 @@ jobs:
     - name: Update PyPA packages
       run: |
         # Get the latest pip, wheel, and prior to Python 3.12, setuptools.
+        wget -P ~/.cache/pip 'https://files.pythonhosted.org:443/packages/c7/c3/55076fc728723ef927521abaa1955213d094933dc36d4a2008d5101e1af5/wheel-0.42.0-py3-none-any.whl'
         python -m pip install -U pip $(pip freeze --all | grep -ow ^setuptools) wheel
 
     - name: Install project and test dependencies