Most supercaps have very low current draw allowances
This is no longer true. These days, supercaps are being used to IMPROVE the pulse current characteristics of batteries that are already relatively powerful. Of course, the supercaps intended primarily for things like memory backup power still exist as well, so you do need to try to find specs for your particular supercap. If it's one of those freaking huge "BoostCaps" that have been appearing on the surplus market, a boost regulator might be reasonable.
One of the super-cap vendors (cooper bussmann) has a "capacity calculator" spreadsheet that you can download and plug in values like "charge voltage" (2.3V), minimum useful voltage (1.8V?), time required, and etc, and it will give you the unknowns: http://www.cooperindustries.com/content/public/en/bussmann/electronics/resources/library/apps_notes_technicalinfo.html
it can be charged up from 5V,
Um. Not recommended if it's a 2.3V supercap!!
The Uno is not a low-power board, and has several components that require 5V. The ATmega328p processor itself has a maximum frequency specification that depends on the power supply voltage. The Uno has a 16MHz crystal, and the lowest operating voltage that will support 16MHz is about 4V. It can operate down to 1.8V at 4MHz, but running at that speed would require board and arduino core modifications.