In America, you don't "connect to" your earbuds, you "put them on". Although the earbuds go in your ear, I rarely hear people say you "put them in". This may be different in other English speaking countries.
So I would say:
"Hold on, let me put my earbuds on."
Then when you're done, you say:
"I'm listening through my earbuds now. Could you repeat what you said earlier?"
I you want to use "connect", it usually implies digital earbuds, such as Bluetooth earbuds, which DO NEED to be "connected" (paired) to your phone. It's not you who connect "to" your earbuds, but it's your earbuds that connect to your phone!
So if the earbuds require Bluetooth, you would say:
"Hold on, let me connect my Bluetooth [earbuds] [to my phone] first."
or
"Hold on, let me switch to my Bluetooth [earbuds]."
and afterwards,
"I'm now using my Bluetooth [earbuds]."
For Bluetooth earbuds, saying "earbuds" is optional.
For wired earbuds (let's say with the 3.5mm jack), you would say "plug in":
"Hold on, I'm plugging in my earbuds to my phone."