Voting systems aren't fragile at the moment
In the US the actual voting is run by part time volunteers with the county workers organizing and supervising the ballot. I work as a Precinct Inspector which gives me a close look at how systems work in our county (elections are organized by county in the US). Up to the last election we used one of two systems, one being a optical card reader, the other being a touch screen system (required because it was ADA compliant). The vast majority of ballots were cast on optically read cards. The machines that tabulate the votes are hacker proof because their technology was so old that there's no way into them. Any weakness would be in the removable memory pack that kept the results but even that was secure because of statistics and the backup of the ballot cards. Starting next year we're going over to these new voting systems. I'm skeptical that they will be as secure as the older systems but I'll reserve judgment until I start working with them.
The reason why we need these systems is that we hold numerous elections on the same day. An election like last year's midterms may require two cards per voter (filled on both sides) and if nothing else those cards are *heavy*. The real weakness in the system isn't the voting machines, its the postal ballots (and, as ever, voter suppression in certain key states). You don't have these problems in the UK so I'd just stick with a bit of paper with an 'X' on it.