the old carts were on EMS 32M smart carts. the carts to which you refer (the emulator carts) i'm guessing are the 64M smart carts, made by the same company.
you'd get the same effect if you got a cart and had someone else flash it for you, like the vendor. this would bypass any issues with needing to plug it in. apart from making backups, which is something the 32M carts will do ONLY with the EMS Transferrer devices.
tracking down an original cart will get you a 32M cart, with a very early version of LSDJ on it.
probably not worth it... you wont escape the issues you fear. instead, you'll have a non-USB (still) EMS-brand very early version of LSDJ cart, which you can't make backups from UNLESS you've got a Transferrer device which REQUIRES your computer to have a parallel port... and then you're back to the issue of using the software (different drivers but same essential thing).