Now that you know that there's really no age too old to start singing, you can confidently move forward in your efforts. There is no age limit when it comes to learning to sing. Learning to sing requires motivation, concentration, commitment, time and patience, which are attributes commonly found in older students. In addition, the human brain is capable of learning in any physical barrier that can be overcome with dedication.
The male voice is loudest around the age of 40, so nothing. In my opinion, go with a one-hour class every week. If you did that for a year, I'm sure any good singing teacher would have you quite confident in your ability. A year of classes with a good singing teacher is more than enough to make someone pleasant to listen to, but if you want to be really good, it will probably take longer unless you have a good ear.
An early sign of vocal damage is a sore throat, so it's important to prepare your voice properly for singing. A good teacher will make learning faster and, if you sing demanding music, the teacher can teach you techniques to protect your vocal cords. I will explain in more detail why I think older students possess all the qualities necessary to learn to sing and why the brain is capable of doing so. If you haven't had the opportunity to learn to sing in your entire life, then there's another reason why you should consider starting now.
There are a number of changes that occur within the body as you age that will affect your singing voice, but these changes won't stop you from singing. The Stack Exchange network consists of 180 communities from Q26A, including Stack Overflow, the largest and most trusted online community for developers to learn, share their knowledge and develop their careers. I made things much more difficult for myself by not enjoying the learning process and being too critical of myself. My other concern is that if I can only afford one lesson a week is enough, especially at this point in the game.
So if you've started to notice that your memory isn't what it used to be, then learning to sing is a good idea. If you're ready to start your journey in learning to sing, you should look for a good singing teacher to guide you through the process. One of my students is in almost the exact same situation as you, he is 30 years old, he already plays guitar and mandolin and he is learning to sing so when he sings in his bluegrass jams it can sound decent rather than horrible. Just to further convince you that you can start singing at any age, here's some information about why your body and brain are able to learn to sing, even if your mind isn't sure.
You didn't mention what kind of music you want to sing, but most people just learn to sing by singing.