Edit (11/14): As far as I know, there are no significant risks to having both a wired and a wireless network connections open at the same time, beyond the risks implied by each one individually.
There are risks with having a machine connected to both an internal-only network and to the Internet: it partly defeats the purpose of having a firewall to separate your internal-only network from the outside Internet. The purpose of a firewall is to have a single chokepoint that controls the security perimeter. If you have a machine that's connected to both the inside and the outside, that machine now becomes part of the security perimeter. For instance, if that machine gets compromised, now your entire internal network is exposed to the attacker. For this reason, it's generally not recommended to connect machines to both networks.
If malware compromises this machine, the malware could set up a route like you mention -- but if malware compromises your machine, it could just directly start attacking your internal network without modifying any routes.
I want to emphasize again the importance of being clear in your mind about which aspect of the networks is relevant. For instance, in this case, I think the "wired + wireless" part is not a concern, but "internal-only + Internet-connected" part is a concern (and "not-under-your-control + under-your-control" would also be a concern). I don't know what you mean by "regulated", so I'm ignoring that aspect.
I don't think there's any need to go around creating/imposing some special restriction on your hosts to block access to wireless while they're connected to a wired network.
There is one mitigation I can mention to you, for consideration. One organization I'm familiar with has two separate internal networks: one network for non-mobile devices, and a second network for mobile devices (laptops, smartphones, etc.). The first network has full access to our internal servers, and only supported wired (not wireless) access. The second network has semi-limited access to some (but not all) internal services. It supports both wired and wireless access. All mobile devices (laptops, etc.) are automatically directed to the second network (even if they connect via Ethernet, they are still connected to the second network). The purpose of this mitigation is to reduce the spread of malware: empirically, sysadmins noticed that people would often take their mobile devices while traveling, get exposed to malware from some other network (e.g., at a hotel that doesn't have our firewalls), get infected, then bring their device back home and connect to one of the internal networks and infect other internal machines. This isolated-network design is intended to slow down the spread of such malware. Today, it might not be as effective or realistic, but it's something you could consider. However, the best way to mitigate your risks will likely depend intimately upon your particular business and your particular situation.
My earlier answer to the original question:
This question is confusing. It seems to me you are confusing/conflating several different concepts:
Communication medium: wired vs wireless.
Connectivity: an internal-only network (that can't reach the external Internet) vs a network that's connected to the Internet.
Administrative control: a network under your organization's control, vs one that is not.
These are independent features. They're not tied to each other. Your question seems to start from a faulty premise: it seems to equate, e.g., wireless with "not under your administrative control and connected to the Internet" while equating wired with "internal-only and under your control". If that is truly what you were thinking, it is a misconception. You can have a wireless network that is either under your administrative control, or not; and is either connected to the external Internet, or is not. You need to analyze the effect of each of these aspects separately.
Each independent axis affects the risk in a different way:
A wireless medium is potentially riskier, because it enables eavesdropping, interception, and message injection by anyone who is within radio range. This risk can be mitigated or eliminated by using proper security, e.g., WPA2 with a strong key.
Internet connectivity adds risk, because there is the potential that people visit a malicious site and get attacked (or otherwise are attacked by malicious entities on the external Internet). This risk can be somewhat mitigated by using firewalls, endpoint protection, and device hardening, but only to a limited extent.
Use of a network outside of your administrative control adds risk.
So, what should you do? You should figure out what your business requirements and needs are. You should identify what the threats and risks associated with the networks are. Then, based upon a cost-benefit analysis, identify controls to mitigate those risks so the risk is at an acceptable level, given your business's requirements and risk tolerance. Saying anything more specific will depend heavily upon your particular organization and your particular situation.