In practice you'd find that most staff would be pragmatic about it and wouldn't pull you up for travelling without your wife, provided you can show both tickets. However, there is always the chance of encountering a "jobsworth" who enforces the requirement for both cardholders to actually travel.
Better to play it safe - in the first instance, ask the retailer you bought your tickets from whether they're willing to to give a fee-free refund on your original tickets if you buy new undiscounted ones. If they say no, try asking the TOC(s) you'll be using whether they'll give you permission to travel on your own. You could also try excessing away the Railcard on your original ticket at a ticket office.
Unfortunately all of these involve discretion, and there's no guarantee of this being exercised. If none of the above work out, you'll just have to buy a new ticket and see if you can get a refund on the old one (this will depend on whether it's an Advance or walk-up ticket, and if the latter, whether the ticket is worth more than the admin fee of up to £10 that the retailer may charge).
Bear in mind that one thing you definitely are entitled to, regardless of whether you have an Advance or walk-up ticket, is to change your journey to another date of your convenience. This would attract an admin fee of up to £10 depending on the retailer, and you'd have to pay any fare difference. But it should at least mean that you don't totally waste the value of your ticket if you have an Advance.