There are two of us already on the team and have some knowledge of programming but no qualifications. Do you think we will be disadvantaged by not having a technical co-founder?
Depends on what you want to do and how matching the skills of your collegs is. If you plan a huge social platform and your collegs have only little PHP skills, you probably should go looking for one. If your collegs have already made webapps with Java or with any other language, they probably know what they are doing and you don't need one.
Based on the information you gave us, it is very difficult to say. I even just guessed you do something on the web.
I think it is helpful to have somebody on the team that is able to handle technical questions as well as add credibility to the long term success of the business. I am sure one of the questions every investor would as is who is backing up this business on the technical front?
If may I will put a little spin to this question as ask:
Do you think its better to have a co-founder with equal shares, or will the skilled and qualified technical person who work for your as a contractor suffice? (Considering the software has been programmed by the same individual on contact basis)?