Accidentally bought OMTP headphones for a CTIA phone, what now? I made the mistake of buying the old Sony Ericsson MH1-LB LiveSound headphones for my Sony Xperia Z1 phone, thinking the two would work together, sound, microphone, controls and all.

I have found out that this is not the case, and the reason is that the headphones use a standard called OMTP, while my phone uses another standard called CTIA, which basically just switches a couple of things around - as far as I've understood.

What options do I have now? Should I start looking for other headphones, or is there a way to use these headphones with my phone after all? 

I've looked around on Amazon, and found CTIA to OMTP adapters, branded as "iPhone to (older) Android converters". Is it safe to assume that these can be used the other way around as well, that is, to convert OMTP to CTIA? The way i see it, the cable just switches around the mic and earth components, so it should be able to work both as CTIA to OMTP, as well as OMTP to CTIA. Is this correct, or am I missing something?

In case someone would like to know, this is the adapter I've been looking at.

PS: In case an adapter like this can work as an OMPT to CTIA adapter as well, people are welcome to leave a comment, if they know a similar but better product. Note however, that this is not the purpose of this question.
I think the OP has already bought a converter and is enjoying the MH1, but in case someone else stumbles upon this, I have Xperia Z2 and an old MH1. I use a Sony Ericsson EC250 adapter. Everything on the MH1, including the mic and all four buttons are working fine. The converter is basically a CTIA to OMTP converter for old phones, but those converters work in both directions. You don't specifically need the EC250. Any OMTP to CTIA or CTIA to OMTP converter should work.