6'2" guys don't look stupid with guitars, so why would you look stupid with a shortscale bass....which is larger than a guitar? Go for it. I'm 6'1" and play a Little Martin travel guitar when I'm out of town. If anything it makes me look beast.If I don't look stupid with a shortscale guitar, you don't look stupid with a shortscale bass.
Oh yeah - also there's gonna be some guy coming along shortly who will make a fuss about tone and tell you that he has barbie hands but still toughs it out on a long scale. Tell that guy you'd still like the use of your hands in 20 years for more intricate tasks than just holding the instrument longingly...
LOL! I'm a short gal with Barbie hands who played only 32s for a long time. I recently picked up a couple of 34s on Ebay and much to my surprise, neither has given me problems. My main issue is neck thickness. Chunky necks of all scales make my hand cramp up something awful, but I can play thin-neck 34s all night long without needing to eat Aleve like candy.
One of the 34s I bought is an Ibanez 5-string and I am totally in love with the neck. I was sure that the wider fingerboard would give me trouble (I only started playing 5-string a few months ago after taking a year to get used to a 4-string tuned BEAD), but so far I've been fine. To the OP: Try out a bunch of basses that vary in scale length, neck width, and thickness. Your hands will tell you what works best.
My basses vary in size from a custom Stoneman copy of a BC Rich Beast with a long body (it's the points!) to an SX Gypsy Rose P-bass copy whose body is about the same size as a Strat. I hear a lot of odd comments at gigs, but never has anyone come up to me and said something about my bass size in proportion to my size.