I can say likely the "best" option is to just wait for a new regulator to arrive (got a local brew club you can borrow one from?) and carbonate the beer the right way.
But, assuming you HAVE to have this beer NOW
The CO2 you have in there presently isn't going to cut it- even if you shake it. At best, you'll have pretty flat shaken up beer (which ...
There are small home kegerators on the market.
For example, this home kegerator can be installed even in a tight corner of your house https://www.beveragecraft.com/home-kegerator-full-size-includes-1-tap-tower/ And what I like about it you can move it around on casters.