Even though like 98% of my portfolio is BTC, I would still like to be able to store alts as well. Another solution could be having 2x HW, but that's also hassle. J
If 98% of your portfoli is bitcoins, 2% for altcoins, it's posisble to store altcoins in many wallets like Metamask, Myetherwallet, and more. They are not safe like hardware wallets but if you don't want to store them in a same hardware wallet of bitcoins, don't want to store them in exchange accounts, it's your only method. If you choose this method, then you will have many choices as many wallets are available for altcoins.
If your fund is big, I don't see how you can not afford to spend money for purchasing a second hardware wallet that is used only for altcoin storage.