Before you opt for any tattoo placement, you should always consider the long term tattoo after-care. First, if you have hairy arms, back, or legs you may want to consider a different tattoo placement.
With that said, you may still want tattoo sleeves and by all means you should go for it, if that's your style. A few things to keep in mind: your job, sun exposure, and of course, body hair.
Removing Body Hair
There are several permanent and temporary body hair removal methods.
Some men wax their arms, as this leads to a smoother surface for a longer period of time, up to six weeks to be exact. The downside is that your body hair will have to reach a length of at least a quarter inch long in between waxes, which equates to three-four weeks of growth. In addition, body waxing is the more painful approach. Is it bearable? Oof course. After being fully tattooed, waxing pain should be the least of your worries.
Shaving with a razor is a quicker and more affordable approach that will lead to smooth results for several days in between. On the downside, you will have "stubble" every few days that you'll need to maintain by shaving several times weekly.
Shave gently in the direction of hair growth to avoid ingrown hair.
There are other forms of hair removal, including laser (which is expensive, and can take several visits to be effective), electrolysis and also depilatory creams. Laser treatments require repeat visits, as the initial process yields only a 40-80% success rate. Depilatory creams such as Nair have strong odors some may find offensive, and can be quite harsh on sensitive skin. The last approach, electrolysis, is the most effective yet costly option for permanent results.
If you are in-between weighing the pros and cons of each hair removal method, I would suggest body waxing. For this service you should always go to a professional esthetician who has been properly trained and licensed in your state.
Protecting Your Tattoo Sleeves
In addition to hair removal, watch out for the sun. Your tattoo sleeves should be covered up to help prevent fading. This means long-sleeved, lightweight cotton shirts in the summer and a mild SPF daily, even when you are driving in the car. Not only will you protect your body art, but you'll also help to prevent skin cancer.
While some people find this overall maintenance of hair removal and sun protection too much to bear, others go into tattoo sleeves with the understanding that their body art is an investment and should be protected to look its best.
In the end, it's up to you. There are plenty of faded and old tattoos that would look much better had they been diligently cared for over the years. Sometimes people just live in the moment and deal with the circumstances of their lifestyle choices later. Que sera, sera!
Lastly, to answer your question: If you are worried about the lady in your life or other random women questioning your choice to shave or remove body hair, I would suggest you explain your reason why. They may only find it strange if they don't understand it, or if you don't mention it.
When she starts rubbing up your arm for the first time, you may want to say, "By the way, I have stubble because I shave to enhance the vibrancy of my body art." No shame. Just don't make her guess or ask her friends because that's what makes it weird. Full disclosure clears up a lot of questionable activities.
As long as you have an understanding that your body art will fade over time, and that body hair will hinder the brightness and visibility of your tattoo and its small details, you can make educated choices in both tattoo placement, tattoo aftercare and protection. Best of luck!