It all depends on your situation and goals.

Money is so cheap here that leveraging as much as you can is often the best option for many people. Your capital is usually better deployed elsewhere. But if you are keeping it in cash, depending on the interest you are receiving, this may not apply to you.

In transferring it over, you are taking a long position on FX, so you should keep this in mind.

In terms of the transfer itself, if going from your account overseas to your wife’s account here, you may be subject to gift tax. Transferring it to yourself is probably the best option. You will almost certainly get asked the purpose (and need to disclose this when transferring anyway). You may want to have the paperwork in order to show the cash is your savings from before coming to Japan and not, for example, an inheritance or gift (unless you disclosed and paid tax on it at the time).