Hi there, you are through to Dr Linda.
These are both NSAID (non steroidal anti-inflammatory) medicines and can certainly be substituted for one another and you should find they provide roughly the same pain relief.
However, it is usually recommended that we have a 5 day wash-out period in between changing NSAIDs. During this time, you may wish to manage the pain with other pain relief medications, such as an opioid like Tramadol.
However, do discuss this with Bailey's vet as they may feel the risk is low and they would rather have him on an NSAID at all time (if his arthritis is quite bad) so may want you to just continue the meds without a gap at all.
Do keep an eye out for symptoms such as vomiting, diarrhoea or blood in the poo.
6 monthly blood tests are recommended for dog on long-term NSAIDs.
Do continue with the Yumove, which will not interfere with the NSAIDs.