The files you deleted in /usr/share
come from the installed packages. The only way to get them back (short of active data recovery) is by reinstalling all the packages that had files there.
Luckily, this can be done fairly easily but it's going to involve an amount of downloading. First, let me illustrate the mess. Here are all the packages that have files in there on my system:
$ dpkg -S /usr/share/applications | cut -d: -f1 | tr -d , | fold -w 80
aftershot3x64 aisleriot alacarte apport-gtk apturl-common audio-recorder baobab
bless california cheese chrome-gnome-shell cubic dbeaver-ce dconf-editor deja-du
p dolphin-emu eog evince evolution-data-server-online-accounts file-roller firef
ox font-manager gcr gedit geoclue-2.0 gimp gkbd-capplet gksu gnome-bluetooth gno
me-boxes gnome-calculator gnome-calendar gnome-characters gnome-color-manager gn
ome-contacts gnome-control-center gnome-disk-utility gnome-documents gnome-font-
viewer gnome-logs gnome-mahjongg gnome-maps gnome-mines gnome-music gnome-photos
gnome-screenshot gnome-session-common gnome-shell gnome-software gnome-sudoku g
nome-system-monitor gnome-tweak-tool gnome-user-share gnome-weather google-chrom
e-stable handbrake hexchat htop hugin ibus ibus-table imagemagick-6.q16 im-confi
g i-nex inkscape libreoffice-calc libreoffice-common libreoffice-draw libreoffic
e-impress libreoffice-math libreoffice-writer meld menulibre mono-runtime-common
mutter nautilus network-manager-gnome nvidia-settings printer-driver-foo2zjs-co
mmon python2.7 python3.5 simple-scan software-properties-gtk steam sublime-text
terminator totem transmission-gtk update-manager usb-creator-gtk uzbl vim-common
vino virtualbox-5.1 vlc xdg-desktop-portal-gtk xterm yelp
To reinstall all of those we can just run. This should work on your system too.
sudo apt install --reinstall $(dpkg -S /usr/share/applications | cut -d: -f1 | tr -d ,)
Files from /usr/local/...
aren't package-controlled. I can't help you there.