diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 9b0ec697..e157fe20 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -41,11 +41,11 @@ jobs:
         include:
           - os: ubuntu-20.04
           - os: ubuntu-22.04
-          - os: ubuntu-20.04
+          - os: ubuntu-22.04
             tool: major.minor.patch
-          - os: ubuntu-20.04
+          - os: ubuntu-22.04
             tool: major.minor
-          - os: ubuntu-20.04
+          - os: ubuntu-22.04
             tool: major
           - os: macos-11
           - os: macos-12
@@ -134,7 +134,7 @@ jobs:
           apk --no-cache add bash cargo
         shell: sh
         if: startsWith(matrix.container, 'alpine')
-      - uses: actions/checkout@v3 # TODO: actions/checkout@v3 requires glibc 2.28+
+      - uses: actions/checkout@v3 # TODO: actions/checkout@v4 requires glibc 2.28+
         with:
           persist-credentials: false
       # cross attempts to install rust-src when Cargo.toml is available even if `cross --version`
@@ -146,6 +146,21 @@ jobs:
         with:
           tool: ${{ steps.tool-list.outputs.tool }}
 
+  test-no-cargo:
+    runs-on: ubuntu-latest
+    timeout-minutes: 60
+    container: ubuntu:22.04
+    steps:
+      - uses: actions/checkout@v4
+        with:
+          persist-credentials: false
+      - name: Generate tool list
+        id: tool-list
+        run: tools/ci/tool-list.sh >>"${GITHUB_OUTPUT}"
+      - uses: ./
+        with:
+          tool: ${{ steps.tool-list.outputs.tool }}
+
   manifest:
     runs-on: ubuntu-latest
     timeout-minutes: 60
diff --git a/tools/ci/tool-list.sh b/tools/ci/tool-list.sh
index c96ee262..1fc5b275 100755
--- a/tools/ci/tool-list.sh
+++ b/tools/ci/tool-list.sh
@@ -72,6 +72,10 @@ esac
 tools=()
 for manifest in tools/codegen/base/*.json; do
     tool_name=$(basename "${manifest%.*}")
+    # cross -V requires rustc
+    if [[ "${tool_name}" == "cross" ]] && ! type -P rustc &>/dev/null; then
+        continue
+    fi
     case "${host_os}" in
         linux*)
             for incompat in ${incompat_tools[@]+"${incompat_tools[@]}"}; do
@@ -120,14 +124,17 @@ case "${host_os}" in
         fi
         ;;
 esac
-# cargo-watch/watchexec-cli is supported by cargo-binstall (through quickinstall)
-case "${version}" in
-    latest) tools+=(cargo-watch watchexec-cli nextest) ;;
-    major.minor.patch) tools+=(cargo-watch@8.1.1 watchexec-cli@1.20.5 nextest@0.9.57) ;;
-    major.minor) tools+=(cargo-watch@8.1 watchexec-cli@1.20 nextest@0.9) ;;
-    major) tools+=(cargo-watch@8 watchexec-cli@1) ;;
-    *) exit 1 ;;
-esac
+# cargo-binstall requires cargo
+if type -P cargo &>/dev/null; then
+    # cargo-watch/watchexec-cli is supported by cargo-binstall (through quickinstall)
+    case "${version}" in
+        latest) tools+=(cargo-watch watchexec-cli nextest) ;;
+        major.minor.patch) tools+=(cargo-watch@8.1.1 watchexec-cli@1.20.5 nextest@0.9.57) ;;
+        major.minor) tools+=(cargo-watch@8.1 watchexec-cli@1.20 nextest@0.9) ;;
+        major) tools+=(cargo-watch@8 watchexec-cli@1) ;;
+        *) exit 1 ;;
+    esac
+fi
 
 # sort and dedup
 IFS=$'\n'