There are two sides to the problem, the OS4K and the handsets.
First you need the OS4K to provide SIP connectivity (which should work to any SIP device like a Unify WL3 or wired handset, or any other third party SIP device/soft client). If you have physical shelves you need (a) an STMI card configuring for SIP extensions and (b) some SIP extensions adding in the telephony DB. If you have a software shelf like an Access 500 or something running in ESX, the STMI becomes a vSTMI but the principal is the same... the (virtual) card would need to be added, and some SIP extensions added into the DB. The STMI or vSTMI is given an IP address and your SIP client would register to it.
Second, you need the WL3s configuring to register on the STMI card. This requires the programming module to configure the phones (an Ascom'ism). Other SIP handsets will work but the WL3 uses Unify firmware and is fully supported. In your post you say the OS4K has the capacity to support wifi handsets. To be clear, the OS4K is supporting SIP handsets which happen to register to STMI over your wifi. 4K neither knows nor cares about the WLAN.
There is not a large amount of work here, configuring each physical handset will be the brunt of it. You could do that yourself once the OS4K is configured for SIP. Some of your cost may be for a physical STMI card which you need to provide the SIP connectivity.
>>Unify still active as a subsidiary of Atos now. Honestly not an OEM that readily rolls off the tongue when talking about VOIP in the UK
Siemens now Unify VOIP kit is rock solid, it'll do the job when it's configured right - and when your network is up to scratch. Don't forget that bit. Make sure your QoS is configured on the OS4K, the handsets, and in your network.
Training department is now in Milton Keynes.