Famicom in a Color TFT monitor
There are a few clones out there that are inside their own TV (such as the Dongsheng clone.) From the looks of it the screen on this thing is very small (use the controller as a reference.) But as far as I know it is still a TV, so technically I guess it shouldn't classify as a handheld. TV can also be used as security monitor, and has outputs for various things like DVD player, VCR, etc. I have no idea where to get one of these.
Found some tech specs for this system. It's a TFT monitor with 76 built in games (no cartridge slot.) Apparently there's a built in speaker but also an internal FM transmitter sends the sound to an external radio, so you could listen to it through your home stereo. Looks like a pretty cool machine, but the auction was for $109, waaayy to much for a famicom clone like this. If I saw one for $60 to $80 I might think again.
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5.6 LCD TFT Wide Format Monitor
76 Video Games Built In
FM Transmitter sends Audio Wirelessly to Radio
A/V Input for External Video Source
Credit Card Size Remote Control
Full Function On Screen Menu
Diversity Antenna Inputs
Dimensions: 5.5 H x 7.5 W x 1.5 D