Honestly I'd be somewhat nervous in your position. I do genuinely sympathise with the predicament of financial uncertainty and limited funds given the craziness that this year has thrown at many businesses, but aside from section 4.11, I could see this potentially causing issues in relation to 1.1.4 - providing neither a trained internal person nor a suitable contract service may raise questions about the resource provision requirements of the standard.
As for the in-house approach, this is acceptable but there is a clear obligation for it to be undertaken in accordance with clause 4.11.3 - you need to be able to show that you have "trained and competent staff with sufficient knowledge", and there is also a requirement for resource etc.
If you have very detailed reports from e.g. the last full inspection then you might be able to use that as a guide, but unless you are very competent in this area it will be difficult to really undertake this yourselves to a suitable standard, and I would still be doubtful that it would satisfy the requirements of the section.
Perhaps a more sensible compromise might be to make an appointment with the pest management company to restart the service, but to kick off with a review including a reassessment of the visit requirements? If you have a demonstrable history of few/no issues then perhaps such a regular service is not needed, and particularly given that you've posted this in the BRC Packaging forum so the implication is that you're not actually handling food products and thus would be of fairly limited attractiveness to most pests?
I've no idea of the site structure/fabrication/location, but to me a scheduled visit every two weeks sounds like it could be more than is necessary? It's perfectly fine to reduce visit frequency (I've done this at BRC certified sites), but only if you have the data to show it is not putting your facilities/products at risk, and that the conclusion is agreed by someone who can prove that they know what they're looking at.