Using your Android 4.4.4 browser (which is likely very slow), navigate to APKMirror using Chrome or Firefox Legacy. Download the YouTube_17.29.34.apk file to your folder.
Because the official app often fails to load even after a manual APK installation, third-party "clients" are currently the most reliable way to watch YouTube on Android 4.4.4. Youtube Android 4.4 4 Download Apk