So your tubing is not 1/4 - 1/8? Standard LFS tubing has a larger ID than 1/8, but CO2 tubing is generally 1/4 by 1/8, or, if it's Asian, ADA included, sometimes 6mm/4mm. I'd switch to 1/4 by 1/8, but if it's 6/4mm, I'd go with Swagelok/Parker/clone (there are many) compression fittings.
However, the idea of going with 3/16 may work, especially if you're using nonstandard tubing size. Still, unless you're planning on going specifically with ADA equipment, I'd switch everything to 1/4 by 1/8, tubing and fittings included.
Compression fittings are the most dependable. Nonplastic components are the most dependable. 1/4 by 1/8 tubing and compression fittings are the most standard in our hobby.