You're going to lose quality with converters but for what you're using it for that may be your only option.
When you download a Youtube video it's going to be in flash flv. format.
You can use this site to download the youtube videos: http://keepvid.com/
And here's a link to download a flv to mp4 converter: http://www.brothersoft.com/doremisoft-free-flv-to-mp4-converter-169691.html
Dell trusts Brothersoft so I know it's a legit download. No viruses, at least.
Hope that helps. If you have any questions, let me know. I've done this before with my own phone.