What do you mean by "paper tickets"? TfW guards are capable of printing paper roll tickets, but not CCST. They can print tickets that have already been bought, using the collection reference, but obviously not those that have to be issued as CCST. Would they be able to print the OP's ticket as a paper roll ticket?
That's a fair question; CCST and PRT are separately enabled fulfillment methods and I'm not sure whether Merseyrail veto PRT too (since it is effectively a printed eTicket), or just actual eTickets. If they veto PRT then that would prevent the tickets from being collected from the guard.
I note that most journeys only seem to have a fairly short connection at Bidston.
Trains from Bidston to Liverpool are every 15 minutes for most of the day so it's hardly the end of the world if you end up taking the next one. Admittedly more of an issue in the evening or on Sundays when it's only every 30 minutes.
Will the OP have time to collect the ticket there, if it involves going to the booking office, without missing the connection?
Probably yes, but there are no guarantees.
Are there barriers there?
No and the ticket office is on the island platform if I remember correctly.
I regularly have a similar problem travelling from the Cambrian Coast to South London stations, as none of the stations near me have ticket issuing facilities. I was advised that I was allowed to travel without a ticket to the first station where I could buy the ticket without interrupting the journey. However, I imagine that Merseyrail could take exception to someone travelling without a ticket.
If there are no ticketing facilities available at the station where the journey is started, you are entitled to board the train without a ticket. That extends to subsequent connecting services if there was no opportunity to buy a ticket on the train (e.g. the guard did not come through) and insufficient time when changing trains. If the guard does come through but can't print your ToD booking you would still need to buy a new ticket, is the issue.
However I agree that it would be better to collect the ticket before reaching Liverpool, to avoid any potential difficulties at the barriers. We have seen plenty of Merseyrail Penalty Fares be issued for not collecting a ticket bought via ToD, and based on the industry's notoriously poor track record you cannot necessarily expect their RPIs to work to the above rule.