Funny, I know it isn't good for you, but I never found DCM to be particular painful to get on my hands. The only time it ever really burned was if I got it on my hand while wearing gloves and then it would seep through the gloves (note, latex gloves are terrible in terms of keeping DCM out), and get trapped on my skin and unable to evaporate.
Getting it under your watch or wedding ring can also be particularly painful.
For the OP, if your major concern is the toxicity of the liquid, I believe you will need to pick your liquid, then find tubing that is resistant to that liquid. There are enough different varieties of clear plastic that you will be able to find something that is resistant to virtually anything you might use. If worse comes to worst, you can use glass.
Alkanes might be the easiest option, something like cyclopentane or petroleum ether. Cyclopentane has a flash point of -37, so you certainly don't want sparks around while you're working with it, but that is slightly better than ether at -45, and the autoignition temperature is higher, 360 compared to 165. And cyclopentane doesn't form peroxides.
The lowest MW ester, methyl acetate, is only a little outside your range (bp 57) and is frequently used as a volatile solvent due to its relatively low toxicity. Somewhat more toxic than ethyl acetate but still very low toxicity for an organic compound.
The low molecular weight amines, like t-butylamine or methyl ethylamine fit the right boiling point range, but tend to be more toxic and are still flammable.
The low molecular weight halocarbons would be the least flammable options, and are also relatively non-toxic, but may be of higher environmental concern.
Hope this helps.